That depends on the game.
One of the most common for Gen 4-5 is the Mausada Method (i'm sorry if i spelled it wrong) where you put two pokemon from two different language games & then breed them. the baby will have a higher chance of being shiny.
In Diamond, Pearl & Platinum, you can use radar chains where you use the poke radar to battle pokemon in the glowing grass. after having defeated over 40 pokemon, the chances of having a shiny pokemon are increased.
In Black 2 & White 2, there is an item you get after completing the national pokedex called the shiny charm which triples the amount of shiny pokemon you find
Sources: here here & here
Hope this helped