Like all previous Pokemon Games from earlier Generations, The Alola Region has plenty of Move Tutors scattered throughout, willing to teach your Pokemon certain moves. Each Move Tutor have something different they are willing to teach your Pokemon, some of which will even require Battle Points or Beach Points in exchange for such services.
Move Tutors
Move Reminder: The Move Reminder, one of the most important characters in all of The Alola Region, can be found in the Pokemon Center at the top of Mount Lanakila. This character will reteach one of your Pokemon a move they have forgotten or you accidentally removed at some point, including Egg Moves they once knew. A new ability for the Move Reminder is to teach your Pokemon a move they can level further along in their learnset.
Move Deleter: The Move Deleter can be found in the Hau'oli City Pokemon Center. But since HMs no longer exist, this character is only useful for certain Last Resort Movesets.
Pledge Moves Tutor: The Move Tutor that will teach any Starter Pokemon from any Region the special Pledge Moves (Fire Pledge, Grass Pledge, Water Pledge) is located in the Hau'oli Mall by Mr. Hyper.
Ultimate Moves Tutor: The Move Tutor that will teach any Fully Evolve Starter Pokemon there Ultimate Move (Blast burn, Frenzy Plant, Hydro Cannon) can be found in the Hau'oli Mall by Mr. Hyper.
Volt Tackle Tutor: After helping the Famous Pikachu fend off a reporter in Hano Grand Resort, his trainer will be willing to teach your Pokemon the move of Volt Tackle. Volt Tackle can only be taught to Pikachu.
Secret Sword & Relic Song Tutor: The character that will teach your Keldeo Secret Sword and your Meloetta Relic Song can be found in the Hano Grand Resort. These moves are necessary to change those given Pokemon's Forms.
Draco Meteor Tutor: The Draco Meteor Tutor can be found in the Seafolk Village Pokemon Center. She will teach this move to certain Dragon Types, as well as Arceus and Silvally when holding the given Plate or Memory that sees them also having the Dragon Typing.
Dragon Ascent Tutor: Also in the Seafolk Village Pokemon Center is the Dragon Ascent Tutor. He will teach your Rayquaza Dragon Ascent, which will in turn allow it to Mega Evolve.
Big Wave Beach Move Tutor: Within Big Wave Beach, you will find a person who is willing to teach your Pokemon a variety of moves in exchange for Battle Points (or Beach Points as they call them). They can teach the moves of Snore, Heal Bell, Electroweb, Defog, Low Kick, Uproar, Bind, Helping Hand, Shock Wave, Block, Last Resort, Worry Seed, Covet, Bug Bite, Snatch, and Recycle.
Heahea Beach Move Tutor: Within Heahea Beach, you will find a person who is willing to teach your Pokemon a variety of moves in exchange for Battle Points (or Beach Points as they call them). They can teach the moves of Iron Tail, Spite, After You, Giga Drain, Synthesis, Ally Switch, Signal Beam, Gravity, Stealth Rock, Iron Defense, Telekinesis, Magnet Rise, Bounce, Role Play, Fire Punch, and Water Pulse.
Ula'ula Beach Move Tutor: Within Ula'ula Beach, you will find a person who is willing to teach your Pokemon a variety of moves in exchange for Battle Points (or Beach Points as they call them). They can teach the moves of Iron Head, Aqua Tail, Pain Split, Tailwind, Thunder Punch, Endeavor, Focus Punch, Icy Wind, Zen Headbutt, Seed Bomb, Laser Focus, Trick, Drill Run, Magic Coat, Ice Punch, and Wonder Room.
Battle Tree Move Tutor: Within The Battle Tree, you will find a person who is willing to teach your Pokemon a variety of moves in exchange for Battle Points. They can teach the moves of Liquidation, Fastro Acid, Foul Play, Super Fang, Outrage, Sky Attack, Throat Chop, Stomping Tantrum, Skill Swap, Earth Power, Gunk Shot, Dual Chop, Drain Punch, Heat Wave, Hyper Voice, Superpower, Knock Off, and Dragon Pulse.