Spoiler:
You have probably heard or seen a picture of them. Pokémon that are different colors than normally seen with. An example of that could be a Metagross with a silver coating and a golden X on it, a dark green Zubat, or a black Rayquaza. The Torchic you may have obtained from Professor Birch may be a lighter colored orange and you may think the game is glitched up, but it isn't. As you can imagine, these occurences are very, very rare. Not very many people even have a shiny Pokémon to begin with. So how do you get them?
It depends on very, very good luck to get a shiny Pokémon. You can find shiny Pokémon in the wild, in eggs, and in the battle tower, which is basically everyplace you can catch a Pokémon save for the Battle Tower in which you won't be able to catch the shinys there. Needless to say, you wont be very lucky if a shiny ends up there. People have said that you can also meet a shiny when in your first battle against the wild Poochyena and Wally's Ralts as well. Basically, like I said, it revolves around how lucky you are. Now the bad thing is that the odds of finding a shiny Pokémon in the wild are 1 in 8,192 battles...all the time, meaning after 8,191 battles it'll still be 1 in 8,192 and not a dead cert that you will get one i.e. not 1 in 1 battles. If you already have a shiny Pokémon and think you'll have a higher chance of getting another shiny if you breed with it, think again. It's still going to have the same odds.
Now you'd think with a Pokémon this rare, it has to have good Individual Values and such. That's no longer the case. Shiny Pokémon are always going to end up with the same odds of good stats as normal Pokémon. They used to have set IV's in the Metal generation, but not in this one.
In the fourth generation, a variety of things have changed in order to allow for the obtaining of Shiny Pokémon. First is a method commonly known as the Masuda Method, named after the game developer and the person who revealed it; Junichi Masuda. This method has you breed two Pokémon. However, one of the Pokémon must be of a different nationality than your game (such as a Japanese Pokémon on an English game). This will lower the chances of hatching a shiny Pokémon from 1 in 8,192 to 1 in 2,048 cutting it by 75% in Generation IV. However, in Generation V, it is boosted even further from 1 in 8,192 to 1 in 1,365.3
It depends on very, very good luck to get a shiny Pokémon. You can find shiny Pokémon in the wild, in eggs, and in the battle tower, which is basically everyplace you can catch a Pokémon save for the Battle Tower in which you won't be able to catch the shinys there. Needless to say, you wont be very lucky if a shiny ends up there. People have said that you can also meet a shiny when in your first battle against the wild Poochyena and Wally's Ralts as well. Basically, like I said, it revolves around how lucky you are. Now the bad thing is that the odds of finding a shiny Pokémon in the wild are 1 in 8,192 battles...all the time, meaning after 8,191 battles it'll still be 1 in 8,192 and not a dead cert that you will get one i.e. not 1 in 1 battles. If you already have a shiny Pokémon and think you'll have a higher chance of getting another shiny if you breed with it, think again. It's still going to have the same odds.
Now you'd think with a Pokémon this rare, it has to have good Individual Values and such. That's no longer the case. Shiny Pokémon are always going to end up with the same odds of good stats as normal Pokémon. They used to have set IV's in the Metal generation, but not in this one.
In the fourth generation, a variety of things have changed in order to allow for the obtaining of Shiny Pokémon. First is a method commonly known as the Masuda Method, named after the game developer and the person who revealed it; Junichi Masuda. This method has you breed two Pokémon. However, one of the Pokémon must be of a different nationality than your game (such as a Japanese Pokémon on an English game). This will lower the chances of hatching a shiny Pokémon from 1 in 8,192 to 1 in 2,048 cutting it by 75% in Generation IV. However, in Generation V, it is boosted even further from 1 in 8,192 to 1 in 1,365.3