Yes it is possible to breed shiny Pokemon but their offspring may or may not be a shiny Pokemon if you want a shiny Pokemon these are the steps you can follow
If you encounter a shiny Pokemon it will be like this
OR Like this
The first image will come in generation 5 and the second in generation 4
1) The PokeRadar:: You use it to chain Pokemon in grass, and the bigger the chain, the higher the likelihood of getting a shiny Pokemon.
a guide for how to use it not mine though
2)Masuda Method :: 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.