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.
The second method of obtaining shiny Pokémon is through the method called "chaining". This method has you carry on a chain on the PokéRadar. As you battle the Pokémon and your chain increases, the chances of seeing a Shiny Pokémon also increases up until you're on the 40th chain where it levels out. Continue the chain and you may see the grass glow instead of shaking. If this occurs, there is a shiny Pokémon there. When you defeat or capture a Pokémon you have discovered with the PokéRadar, the chain begins and you need to follow the chain to other grass tiles to continue the chain. These chains are broken when a different Pokémon appears or you encounter a Wild Pokémon outside of the set grass tiles so it is recommended that you use Repel or other Wild Pokémon prevention techniques. Shiny Pokémon are easily findable with the PokéRadar. If you have found a Shiny Pokémon with the PokéRadar, the grass will shine as opposed to shaking. With chaining, you have the ability to increase the likelihood of finding a Shiny Pokémon. This is done by having a prolonged chain on the PokéRadar. The chances increase up until the 40th Pokémon in the chain. This is calculated with the following formula;
Chance = (14747 - 40*ChainNumber)/2621440(41-ChainNumber)
After each use of the PokéRadar, it requires recharging. This is done by walking 50 steps.
In Pokémon Black 2 & White 2, a new item is introduced called the Shiny Charm. This item, obtained when you have completed the National Pokédex, increases the chances of Shiny Pokémon appearing. As it's a Key Item, when you have the item in your bag, then the chances of encountering Shiny Pokémon in the wild is increased to 300% of normal, making it a 1 in 2,730.6 chance. If, however, you're using the Masuda Method to breed, it reduces it from 1 in 1,365.3 down to 1 in 1024
that covers about shinies