You may have heard of them or even seen a picture of one on the web, but chances are slim that you have never encountered one in the game, and even if you have encountered one, you may not have realized it as you have to pay close attention during the opening of the encounter in order to see the give-away sign that it is a special Pokemon. Once the encounter is underway, the most obvious signs that you have encountered a Shiny Pokemon are the alterations of the opening visual and sound effects of the encounter/battle and its colors.
At the start of an encounter with a Shiny Pokemon the opening sound effect and graphics are slightly different, featuring radiating sparkles and what most trainers call a "sparkling sound effect" that is obvious once you know what to listen for. This effect is also present when you use a Shiny to battle another trainer, or encounter a Shiny in a battle with another trainer.
In the Second Generation games the sound effect and sparkles occur in the opening sequence before the Pokemon voices its call, while in the Third and later Generations these effects happen after the Pokemon voices its call.
The colors on a Shiny Pokemon are different from those of a normal one -- for example the Pidgey that I encountered had a very light olive-green color to its feathers in place of the rich brown that the normal ones have, and the difference in color is very pronounced and obvious, but that is not always the case. A smaller number of Pokemon have only the slightest variation of color and hue so that spotting the stars and hearing the tinkling sound can be the only effective way to identify their unique form!
Shiny status is not a transient status, and what that means is very simple: if a Pokemon is Shiny, it will always be Shiny, even when it evolves into another form, whereas if a Pokemon is not Shiny there is nothing that you can do legitimately to make it a Shiny. Some casual players make use of game altering hardware and software to edit their Pokemon to boost their stats or turn them into Shinies, but doing this will invalidate both your Pokemon AND your cartridge/card for use in Tourney Play! When you sign up for a Tournament at official Pokemon events, your cartridge or card is validated using a special console by the officials, and all of the Pokemon in it are evaluated and checked for tampering.
If you are found to have tampered with any of the Pokemon or even to have an altered Pokemon that you obtained legitimately from the Global Trade Station, your card will be flagged as permanently invalid for Tourney Play! Altering Pokemon, even when it is done nearly perfectly, is simply not worth that penalty, so when it comes to Shiny and Legendary Pokemon, you are better off restricting your acquisition only to trades with people that you can absolutely trust, finding them in the wild, or breeding them yourself!
-- Generation I & II Shiners --
Shiny Pokemon were first introduced in the Second Generation of games, and though the color differences can range from very slight for some Pokemon to very pronounced and obvious for others, the factor that determines whether or not it is a Shiny also differs between Generation II games and the later Generations.
There were no Shiny Pokemon per se in the First Generation, but the method that was used to determine the Shiny status for the first two Generations involved it having capped Speed, Defense, or Special Individual Value Points (IV's), and because of this a Shiny could be traded backwards to a Generation I game and then traded forward to a Generation II game while still retaining its Shiny status. This was often done in order to permit the Pokemon to learn Generation I TM's, assuming that the Pokemon was a member of the Dex of the First Generation.
The odds of encountering a Shiny in Generation II were approximately 1 in 8,192 (which are very long odds indeed!). That being so, it should be noted that Shiny status is a trait, so if a trainer breeds Shiny Pokemon together the odds jump to an astounding 1 in 64 chance, which is almost a sure thing compared to the odds of encountering them in the wild!
-- Generation III and Newer Shinies --
Unlike the first two Generations, the method for determining whether or not a Pokemon is Shiny in the later Generations uses a different system. Since there is no possibility of trading between Second Gen and later games, the Dev's were able to devise a more random and reliable system for Shiny flags that utilizes your Trainer ID Number (a five-digit number assigned to each trainer as they begin their journey into the world of Pokemon), and the Secret ID Number (a second five-digit number that while invisible to the player exists to guarantee that even if two trainers somehow share the exact same name, ID number, and gender, the games will still recognize their Pokemon as being from different trainers). This second number is hidden and cannot be viewed by the player.
The odds of encountering a Shiny Pokemon are 1 in 8,192 but they can be encountered in any location where you can catch Pokemon as well as from eggs that you have hatched, whether you bred them or not. Unlike the Second Generation games, using Shiny Pokemon to breed does NOT increase the odds of obtaining an egg that contains a Shiny Pokemon in the 3rd and later Generations!
While the IV's and stats for Shinies were slightly better in the 2nd Generation games, this is not the case in the 3rd and later Generations, as the Shiny Pokemon in these games always have the same basic chance and spread as regular Pokemon.
-- Generation IV Exceptions --
The 4th Generation Games (Diamond, Pearl, Platinum, HeartGold and SoulSilver) have specific exceptions in them that none of the previous generations contain, and these give a significant advantage to trainers who are seeking to capture or breed Shiny Pokemon! There are two exceptions, and these consist of:
Exception 1: The Masuda Method
Named after Game Freak Director Junichi Masuda, was revealed by Masuda in his regular Pokemon column, and further refined by the folks at the Fan Site "Smogon" (http://www.smogon.com/) and is defined as:
When an egg is bred from Pokemon that are obtained from games that are of different languages from each other (for example an English male from the US version of Pearl and a Japanese female from the Japanese version of Pearl) the resulting egg is four-times more likely to result in a Shiny than otherwise.
The Pokemon can be obtained either through capture, breeding, or trade via GTS, Wi-Fi, or game-to-game, but this does not work if both of the Pokemon are from the same foreign language, even if the game that they are playing in is different from their language. Foreign-language Pokemon that are obtained via in-game trading with NPC's (such as Surge's Pikachu or Meister's Magikarp) also will NOT have this exception because while their language is different, they originated in an English (or whatever your game language version is) game.
The mechanics of this exception are intentional, and were created by Masuda, and the basic function is thus: when a pair of Pokemon are presented to the Daycare Center and the game detects that one of them originated in a game from a language different than that of the game, the odds of their egg resulting in a Shiny are altered from 1 in 8,192 to 1 in 2,048 (which equals a four-times greater chance). This may not seem like a major difference but in the world of statistics it is considerable.
This advantage does come at a cost, however. When breeding with two foreign Pokemon, the 50% chance of passing on one of the parents nature using an Everstone is removed.
Exception 2: Chaining
The chaining method requires you to maintain unbroken chains of detection using the Poke Radar. As you battle the Pokemon and your chain increases the chances of encountering a Shiny Pokemon also increases. As you work through the chains if the grass glows instead of shaking you have encountered a Shiny Pokemon!
To facilitate this method you will want to use as many Repel Potions as necessary in order to maintain the Repel Status throughout the chaining session, to avoid a random encounter that would, in effect, break the chain.
-- The Shiny Attraction --
Despite the fact that Shiny Pokemon are only special because of their appearance, and do not have better stats or special abilities other than what any Pokemon of that type might have, they are still a very sought and desired commodity in the world of Pokemon trainers! On private trade boards you will often see trainers who are willing to trade legendary Pokemon for bog-standard common types as long as they are Shiny, and there is even a subset of trainers who actively compete in Tourneys whose special interest is fielding teams that consist entirely of Shiny Pokemon!
Whether this notion appeals to you or simply represents a curiosity, if you ever do encounter a Shiny Pokemon you should make every effort to catch it, because it could easily be worth one or more of the Pokemon you may still need to complete your Dex, and would make that process much easier through trading it! Be aware though -- in the 12 years that I have been playing, covering every single game in all of the generations, I have only encountered seven Shiny Pokemon in wild encounters and eggs, and of those, I was only able to capture four, and that is considered to be a very good result.