This is my guide to beating the gym leaders and Elite Four.

RESISTENCES:
Water is powerful against rock/ground type.
Fire is powerful against electric and Grass type.
Electric is powerful against water type.
Rock is powerful against Electric type.
Grass is powerful against water type.
Dragon is powerful against fighting and Grass type.
Fighting is powerful against Grass and electric type.
Psychic is powerful against ghost type.
Ghost is powerful against psychic type.

TIP:  Save before each gym battle.  This prevents losing money, and if you're unlucky, you can easily start the game over from your last save point by pressing and holding A+B+SELECT+START.

GYM 1: Pewter City.
LEADER: Brock
POKEMON TYPE: Rock
POKEMON: Geodude lv. 12 ; Onix lv. 14
HOW TO WIN: If you started with Squirtle, this gym should be easy.  Just use water gun.  I suggest you train your Squirtle to level 10+ first so you can confidently knock out Brock's pokemon in one hit with water gun.  If you didn't start with Squirtle, I suggest catching a Nidoran found in the wild to the South of Pewter City.  Train this pokemon to level 12+ and you should be able to take down Brock's pokemon.
REWARD: $1400, TM39: Rock Tomb, BOULDERBADGE.

GYM 2: Cerulean City
Leader: Misty
POKEMON TYPE: Water
POKEMON: Staryu lv. 18 ; Starmie lv. 21
HOW TO WIN:  Squirtle and Bulbasaur will win if they are level 19+ just using their attack sets.  For Charmander, however, you will need to use a different pokemon.  Ideally, you would use an electric type, but in this stage of the game, it is impossible for you to obtain any.  Whatever you do, don't use a ground or rock type pokemon.  Misty will kill that thing in 1 shot every time because rock has a weakness to water.  It takes 4X more damage than a different type of pokemon.  Use the Nidoran one more time.  Be sure not to train the Nidoran too high because you will only need him for these first two gyms.  After this, your Charmander will be powerful enough to take on the remaining gyms with help from other pokemon.
REWARD: $2,400, TM03: Water Pulse, CASCADEBADGE

GYM 3: Vermillion City
LEADER: LT. Surge
POKEMON TYPE: Electric
POKEMON: Voltorb lv. 21 ; Pikachu lv. 18 ; Raichu lv. 24
HOW TO WIN: If you started with Bulbasaur this will be medium difficulty, if you started with Squirtle, this will be hard.  If you started with Charmander, congratulations, you've passed the wall and are ready to start owning this game.  If you started with Squirtle, catch a Diglett or Dugtrio from Diglett Cave to the east of Vermillion and use it against Lt. Surge.  Only the physical attacks can harm you, but none of the electrical ones can.  You should make it through just fine if you started with Charmander/Bulbasaur.
REWARD: $2,400, TM34: Shock Wave, THUNDERBADGE

BADGE 4: Celadon City
LEADER: Erica
POKEMON TYPE: Grass
POKEMON: Victerebell lv. 29 ; Tangela lv. 24 ; Vileplume lv. 29
HOW TO WIN:  Charmander will blast through this gym and I mean blast in the full meaning of the word.  Bulbasaur will make it if you play strategically.  Squirtle's attacks are weak against these grass types, so either use physical attacks or use a different pokemon like Diglett/Dugtrio.  It might take a combination of a few pokemon to make it if you have Bulbasaur/Squirtle.
REWARD: $2,900 ; TM19 Giga Drain, RAINBOWBADGE

REALITY CHECK:  Are all your pokemon within at least 5 levels of each other?  If not, I suggest getting them that way.  Koga is very hard to beat if you have weak pokemon.

GYM 5: Fuschia City
LEADER: Koga
POKEMON TYPE: Poison
POKEMON: Koffing lv. 39 ; Koffing lv.  39 ; Muk lv. 39 ; Weezing lv. 43
HOW TO WIN:  These pokemon are nasty.  They are really hard to beat unless you use brute force.  This is why I told you to get all your pokemon to high levels, because you really need it for this guy.  Koffing, Weezing, and Muk aren't very weak to anything.  So no matter what your starter was, be prepared for a hard battle.
REWARD: $4,300, TM06: Toxic, SOULBADGE

GYM 6: Saffron City
LEADER: Sabrina
POKEMON TYPE: Psychic
POKEMON: Kadabra lv 38 ; Mr. Mime v 38 ; Venomoth lv. 38 ; Alakazam lv. 43
HOW TO WIN:  It's just too easy to beat all of Sabrina's pokemon with a high leveled Charmander (I realize you're little Charmander, Squirtle, or Bulbasaur has probably evolved into a Charizard, Blastoise, or Venusaur already, but I'll just say the starters because you never know who's out there.  It's also fairly easy with the other starters, but you might need some help from your other pokemon.  In my opinion, Mr. Mime or Alakazam are the hardest.  Alakazam's psychic attack does a lot of damage and Mr. Mime is pretty resistant to everything.  Kadabra and Venomoth can be easily taken down with any level 40+ pokemon.
REWARD: $4,300, TM04 Calm Mind, MARSHBADGE

GYM 7: Cinnabar Island
LEADER: Blaine
POKEMON TYPE: Fire
POKEMON: Growlithe lv. 42 ; Ponyta lv. 40 ; Rapidash lv. 42 ; Arcanine lv. 47
HOW TO WIN: If you have a Charmander, great!  If you have a Squirtle, great!!!!!! If you have a Bulbasaur, gre.... Oh wait, BAD! BAD! VERY BAD!  Blaine will crush your Bulbasaur easily and without effort.  This is your wall, Bulbasaur owners.  My only suggestion is to find a high leveled Tentacool or water type (I suggest trying the Seafoam Islands, finding a Dewgong or Golduck or something) and teach it surf.  This shouldn't be too hard to do.  If you have a Squirtle, I suggest you don't worry about Blaine and start worrying about Giovanni, because this is cake for you.  A level 50+ Charmander can get the job done just as well.
REWARD: $4,700, TM38 Fire Blast, VOLCANOBADGE

GYM 8: Viridian City (What?)
LEADER: Giovanni
POKEMON TYPE: Ground/Rock
POKEMON: Rhyhorn lv 45 ; Dugtrio lv. 42 ; Nidoqueen lv. 44 ; Nidoking lv. 45 ; Rhyhorn lv. 50
HOW TO WIN:  Squirtle vs. Rhyhorn and Dugtrio = 1 hit K.O.  Bulbasaur vs. Giovanni = uh oh.  Charmander vs. Giovanni = eh.  Squirtle will dominate, Charmander has seen better battles, but will still make it with help, Bulbasaur will have to rely on the reinforcements:  Vaporeon, Dewgong, Magikarp, whatever.  Nidoqueen and Nidoking are the hardest of Giovanni's pokemon to defeat.  They have high HP and aren't specifically weak to anything.  You'll just have to wail on them.
REWARD: $5,000, TM26: Earthquake, EARTHBADGE, passage to Victory Road/Indigo Plateau for a chance to beat the Elite Four.

CONGRATULATIONS!  You've defeated all the gym leaders!  Now it's time for the hard part.  I'm sure you can manage your way through Victory Road, but I'll tell you a little bit about the Elite Four.  There are four members (obviously) and their names are Lorelei (Ice type), Bruno(Rock/fighting type), Agatha(Ghost/poison type), and Lance(Dragon type.)  Unlike previous gyms where you get a chance to heal after each battle, this is an all out brawl, facing the Elite Four one at a time with no passage back to a pokemon center.  It's just you, your pokemon, your potions/revives, and four trainers with 5 level 50-60 pokemon each. Good luck.

PREP:  If you have a Charizard (I now start saying fully evolved forms because you'd better have it if you want a spitting chance at becoming pokemon league champion) you're extremely lucky because flamethrower is crucial to beating these guys. If you have a Blastoise or Venusaur, you need to go overboard in training your pokemon.

IDEAL PARTY FOR CRUSHING THE ELITE FOUR:
Level 60 Zapdos
Level 60 Moltres
Level 60 Articuno
Level 70 starter pokemon
Level 60 Dragonite
Level 60 Alakazam/Kadabra

I suggest you go into the Elite Four to get large amounts of experience to quickly level your pokemon.  Be sure you're able to beat Lorelei and Bruno first or else you will lose money.

HOW TO GET THIS PARTY:

Having a pokemon with the False Swipe attack is crucial to getting these pokemon with Ultra Balls.
Also having a pokemon with the ability to put pokemon to sleep is also highly reccommended.
You should have at least 20 Ultra Balls if not more in your inventory for each attempt

ZAPDOS:
Zapdos is found in the Power Plant to the south of Cerulean City.  Go East until you hit water then surf down and you will end up at the power plant.  There is a maze to get to the Zapdos, but once you find him follow this procedure:

Save before you approach the pokemon.
Get it into the red (life) and use false swipe to get it down to 1 life. Next, put it to sleep.  Once it's asleep, throw an ultra ball at it. (Despite many rumors, there is no way to increase your chances of catching a pokemon except to paralyze or sleep the pokemon.)  Hopefully the pokemon will stay in the dang pokeball, but it will usually break out. If you  run out of ultra balls or you accidentally kill the pokemon, start over again because the pokemon will not re-appear after it has been defeated.  Follow this procedure until the pokemon is caught.

MOLTRES:

A pokemon with HM04 Strength is required to catch Moltres.

Moltres is found on island One.  Start heading up towards Mt. Ember.  when you hit a fork in the road.  On the left hand side, there are boulders there.  Push them out of the way and follow the path through the cave and you find a boulder puzzle.  Complete it successfully and Moltres is waiting at the end.  Again, save before you approach this pokemon as it will never come back if you defeat it.  Repeat the procedure given to catch Zapdos.

ARTICUNO:


A pokemon with HM04 Strength is required to catch Articuno.

Articuno is found in the Seafoam Islands.  Push 1 rock into each hole using strength.  Once this is done, (I'm making it sound way easier than it actually is) find the area where there were a bunch of boulders and two holes.  Go drop down into the left most hole and surf upwards.  Articuno will be waiting on a small island.  Save before you approach this pokemon.  It will run away if defeated. Repeat the procedure given to catch Zapdos.


The base level of each of the legendary birds are 50.  If you're unable to do the math, you need to raise the levels of each of them by 10 if you want to confidently defeat the Elite Four.

DRAGONITE:

I hate to say this, but there is no easy way to get a dragonite.  If you're feeling lucky, and are good at slots, I suggest you go to Celadon City Game Corner and win the 2,800 coins it costs to obtain Dratini from the prize shop.  There are two other ways to get a Dratini: Buy the coins from the cashier guy in the game corner. (2,800 coins costs $30,000 which doesn't seem worth it to me when you can get them for free from the machines.) Or you can surf around in the Safari Zone and hopefully find one and catch it.  Anyways... your Dratini will evolve into a Dragonair at level 30 and evolve again into a Dragonite at level 55. Once you've evolved your Dragonair into a Dragonite, it's an easy 5 levels seeing as Dragonite is an extremely powerful dragon type.  I suggest you go to the Celadon shopping mart extravaganza place.  On floor 2 you should buy the TM for Hyper Beam. (I believe it's second on the list.)  Teach that to your Dragonite. At level 60, it will learn Wing Attack. Wing attack is freaking awesome because it will take out Bruno's fighting types (except Machamp, but it will do substantial damage) in one shot.  Also teach your Dratini when you first get it the HM Surf.  It takes down rock pokemon with ease.  The reason you have Dragonite is because he can take down 4/5 of Bruno's pokemon in 1 shot and the other in 2.  He can also do some mean damage to the other trainer's pokemon.

STARTER POKEMON:

Go to Island 2 and go to the house with the girl in it up North.  She will teach your starter pokemon an elemental version of Hyper Beam.  The move you learn will be based off your starter.  Charizard will learn Blast Burn, Blastoise will learn Hydro Cannon, and Venusaur will learn Frenzy Plant.  These attacks are great if you're in a pinch.  It's also a good attack to use if you want to finish a trainer or finish a pokemon, knowing that you're not going to use that pokemon again for the next opponent's pokemon.  If you use Blast Burn, Hydro Cannon, Frenzy Plant, or Hyper Beam in the middle of a battle and it doesn't knock out the opposing pokemon, you will have to recharge and the other pokemon essentially gets a free hit on you.  Use this move strategically.  Now all you have to do is raise your pokemon's level to 70 and you'll be set.

KADABRA/ALAKAZAM:

I'm also sad to say there's no easy way to get this pokemon either.  Go crazy with an Exp. Share and an Abra (found in Celadon wild and Celadon prize shop for 450 coins.) At level 16, Abra will evolve into Kadabra.  The only way to get an Alakazam is to trade the Kadabra, so if you have a friend who is playing this game too, tell them to get a Kadabra so you can trade them and end up with Alakazams.  Make sure you train this pokemon to level 60 and make sure it knows psychic because that attack is crucial to defeating Agatha.


RECOMMENDED ATTACKS FOR POKEMON:

ZAPDOS:
Thunder Wave
Thunder
Thunder bolt
Drill Peck

MOLTRES:
Flamethrower
Fly
Drill Peck
Fire Blast

ARTICUNO:
Ice Beam
Blizzard
Fly
Drill Peck

DRAGONITE:
Wing Attack
Hyper Beam
Surf
Fire/Dragon type attack (Dragonite will learn Outrage at level 65.)

ALAKAZAM/KADABRA:
Shadow Ball
Psychic
Hypnotize
Dream Eater

CHARIZARD: (Sorry, I have no experience with the other 2 starters.)
Wing Attack
Flamethrower
Blast Burn
Fire Spin

Okay, that was the hard part.  Now you should be able to defeat the Elite Four using strategic switching and attacks.  Before going into the Elite Four, stock up on revives, lemonade, and hyper potions (full restore if it tickles your fancy, but it's more expensive.)  Keep in mind that if an Elite Four trainer's pokemon gets in the red, they will use full restore about 80% of the time.

THE ELITE FOUR:

CHALLENGE 1:
LEADER: Lorelei
POKEMON TYPE: Ice
POKEMON: Dewgong lv. 52 ; Slowbro lv. 52 ; Lapras lv. 54 ; Cloyster lv. 51 ; Jynx lv. 54
HOW TO WIN: Zapdos is the pokemon to use here.  Use thunder on Dewgong, thunder on slowbro, thunderbolt twice on Lapras, thunder on Cloyster, then switch to Moltres (or Charizard if you have him) and use flamethrower on Jynx. When you win, you get a little over $10,000 for winning.  Then move on to Bruno after you do necessary healing, switching etc.  Switch your leader to Dragonite then head on to Bruno's room.

CHALLENGE 2:
LEADER: Bruno
POKEMON TYPE: Rock/Fighting
POKEMON: Onix lv. 51 ; Hitmonchan lv. 53 ; Hitmonlee lv. 53 ; Machamp lv. 56 ; Onix lv. 54
HOW TO WIN:  Using your Dragonite, surf on both onixes, they will go down in 1 shot.  Use wing attack on the remaining 3 pokemon.  Machamp will require 2 wing attacks. You will get your money after defeating Bruno.  Use necessary potions and put Alakazam in the leader slot.

CHALLENGE 3:
LEADER: Agatha
POKEMON TYPE: Ghost/Poison
POKEMON: Gengar lv. 54 ; Golbat lv. 54 ; Arbok lv. 56 ; Gengar lv. 58 ; Haunter lv. 53
HOW TO WIN:  Use psychic on the Gengars and Haunter.  Don't even mess around with the Golbat and Arbok.  Use Zapdos's thunder on them to kill them in one shot.  They can poison you and that's not good at all.  Use necessary potions and switch your leader to Zapdos.

CHALLENGE 4:
LEADER: Lance
POKEMON TYPE: Dragon
POKEMON: Gyrados lv. 56 ; Aerodactyl lv. 58 ; Dragonair lv. 54 ; Dragonair lv. 54 ; Dragonite lv. 60
HOW TO WIN:  This guy is hard.  Kill his Gyrados in 1 shot with a thunder from Zapdos.  Kill his Aerodactyl by using Kadabra/Alakazam's shadow ball until Aerodactyl is at about half life.  Then use Psychic and he should be through.  I don't know what to say about the Dragon types, but to use brute force and knock them down little by little.  Don't use a fire type for the dragonairs because they know surf.  But I suggest using a hyper beam when you get the Dragonite down to half life.  You should be able to get by with thunderbolts and thunders on the Dragonairs.  Lance will admit defeat and almost crown you Pokemon League Champion. Then he mentions that someone did it before you and his name is GARY! You're not done yet, you have one more challenge.  Use potions as needed and prepare yourself for the hardest battle yet.

CHALLENGE 5:
LEADER: Gary
POKEMON TYPE: All/Against you
POKEMON: Pidgeot lv. 61 ; Rhydon lv. 61 ; Alakazam lv. 59 ; 
IF YOU HAVE A CHARIZARD: Blastoise lv. 65 ; Exeggutor lv. 63 ; Arcanine lv. 61
IF YOU HAVE A BLASTOISE: Venusaur lv. 65 ; Gyrados lv. 61 ; Arcanine lv. 63
IF YOU HAVE A VENUSAUR: Charizard lv. 65 ; Gyrados lv. 63 ; Exeggutor lv. 63
HOW TO WIN: Thunder his Pidgeot, Surf his Rhydon, Flamethrower his Alakazam.  Here's where your birds take a huge role. If you have a Venusaur, send out either Dragonite or Articuno and water down that Charizard.  If you have a Blastoise, get out your Moltres and use the most powerful fire attack you have on the Venusaur.  If you have a Charizard, get out your Zapdos and use thunder on the Blastose.  Use a fire attack on Exeggutor and your special attack on Arcanine after it's life is below 3/4.


CONGRATULATIONS!  YOU BEAT THE FREAKIN ELITE FOUR!  If you want to go back and try again, you have to complete the quest on Four Island first.  While you're there on Four Island, talk to the sticker girl and she will gladly give you the Pokemon League Champion sticker which grants you access to Cerulean Cave where MewTwo lives!  The second time around, the Elite Four will have traded out some of there old pokemon for some new Hoenn/Johto region pokemon.  In addition, their pokemon's levels have all raised by about 10.  

Good luck and have fun!  I hope you become a Pokemon Master!