Welcome to PokeComunity!
There are quite a few ways you could look for shinies:
Soft Resetting: Save in front of an interactable overworld Pokemon, like a legendary or a starter. Encounter the Pokemon; if it's not shiny, press A + B + Start + Select (3rd generation) or Start + Select + L + R (4th and 5th generations). Repeat until desired shiny is summoned.
Encountering: Just run around in grass. If the Pokemon isn't shiny, faint it or run.
Egg Hatching: Just hatch thousands of eggs. There's a tactic called the Masuda Method, which increases your chances of hatching a shiny from 1/8192 to 1/2048 (in the 4th gen) or 1/1366 (in the 5th gen). All you need to do is have the two parents be from games of different languages. For example, you could get a Ditto from a Japanese version of the game and use it when you breed.
