There are many ways in which one can shiny hunt; here are some of the more popular methods: Soft Resetting
Save in front of an interactable Pokemon and encounter it. If it's not shiny, simultaneously press Start, Select, L, and R (Start, Select, A, and B in the 3rd generation). The game will reset and you'll be brought back to where you saved, in front of the Pokemon. Repeat until it shines! Hatching
Put two Pokemon in day care, and hatch eggs until one shines! In the 4th and 5th generations, if the two parents are from different language games (such as an English Bulbasaur and a Japanese Ditto), the odds of a shiny increase from 1/8192 to 1/2048 in the 4th gen and 1/1366 in the 5th gen! Chaining
In D/P/Pt, you can use the Pokeradar to find Pokemon in tall grass. After a chain of 40, the odds are about 1/192. For each number the chain goes up, the denominator of the probability decreases by 200. For example, an unchained shiny is 1/8192. After a chain of 1, the chances will be 1/7992, etc. It stops increasing once you hit a chain of 40. Encountering
Of course, you could go with the classic method: just run around in the grass, caves, or ocean until you find a shiny!
Whichever method you choose, may you have the best of luck and fun hunting!