First there is chaining (search on youtube im sure you'll find some decent tutorials) and if you manage to get your chain to 20+ the chances of a shiny patch appearing is 1/704 of finding a shiny patch where a shiny pokemon is, if your chain is 40+ the chances are 1/204. (at a chain of 40+ just keep reseting the radar untill you see a shiny patch, bring lots of max repels!
Soft reseting: save in front of a pokemon that "attacks when interacted with" and catch it if it's shiny (VERY VERY unlikely) if not (VERY VERY likely) soft reset, press L, R, Select and Start at the same time, encounter the pokemon again to see if it's shiny, do this until it's shiny. this applies mostly to legendaries (Giratina, Rayquaza etc.) but there are also non legendaries like rotom and spiritomb. if the pokemon you're SRing (soft reseting) has 3 catch rate, bring a master ball just in case! the chances that a interactive pokemon is is 1/8192.
Masuda method: get a foreign pokemon from another game cart than yours, like if you have a american game, get a japanse ditto, take the pokemon you want shiny and your foreign pokemon (doesn't necceserly have to be a ditto, but a pokemon you can breed with the pokemon you want shiny) take them to the day-care and let them do "you know what" so you get and egg, and hatch eggs untill you get a shiny (the chances of a masuda mehod shiny appearing is 1/2048 in Gen 4 (D/P/P) and in Gen 5 (B/W) the chance of getting a shiny Pokemon by MM (Masuda Method) was increased even further to 1/1365.3 so that's cool.
Random shiny: just encounter to pokemon you want untill it's shiny then catch it, a random shiny can also be that you're not even looking for a shiny a randomly encounter a shiny pokemon. (also applies to legendaries). the chances of a random shiny appearing is 1/8192.
And remeber to ALWAYS save after catching a shiny pokemon, i lost a random shiny abra by not saving :( luckely you can chain abra tough :)
good luck with your shinyhunting!