Shiny Pokemon are Pokemon that have an altered color scheme. Introduced in the second generation of Pokemon games, Gold/Silver/Crystal Shiny Pokemon are incredibly rare. In fact, you have a 1 in 8,192 chance of encountering a Shiny Pokemon in each wild encounter or egg hatch. Aside from their rarity and different colors, Shiny Pokemon are no different from regular Pokemon; every Pokemon has a Shiny counterpart.
The most popular way of encountering a Shiny Pokemon is simply through chance. Over time and with enough battles, you can hope that you will encounter a Shiny Pokemon or hatch one through breeding. There is no particular trick to encountering a Shiny Pokemon simply through chance, but it is the way that most Shiny Pokemon are found.
The Masuka method is a process in which you breed Pokemon of different nationalities to increase the chance of hatching a Shiny Pokemon. Different nationalities means that you have simply traded a Pokemon with someone from a different country. Then you breed a foreign Pokemon with one of your Pokemon and the egg has a 1 in 1,365 chance of hatching a Shiny Pokemon. This method only applies to the fourth and fifth generation of Pokemon games.
In Pokemon Diamond/Pearl/Platinum, you receive the Pokeradar which allows you to encounter Pokemon in the wild. Using the Pokeradar causes a patch of grass to shake. You can step into the grass to start a wild battle. After the battle, you can use the Pokeradar again to battle yet another Pokemon. With each consecutive battle, the chances of finding a Shiny Pokemon increases until it tops off at 40 "chains." This is made difficult by the fact that you can still be attacked by wild Pokemon while trying to increase your "chain." If attacked, your chain will be broken and you will have to begin again.
You can also give yourself a Shiny Pokemon by using a cheating device such as an Action Replay. By inputting a certain code, you can give yourself any Shiny Pokemon you wish, but be warned that "hacked" Pokemon cannot be used in official Nintendo tournaments. You must also be careful when trading for a Shiny Pokemon; there is no guaranty that the person you are trading with has not used an Action Replay to hack his Pokemon.
