Shiny Pokemon are very hard to receive especially when playing a new game and just randomly encountering Pokemon until you get it. But, there are also little tricks to receive some.
Normally, the chances to encounter one is 1/8192; but 75% less making it 1/4096 when Pokemon X/Y came along. The basic way to get one is just hope until you just encounter one - but that takes forever. Here are some alternate ways:
1) Using the Masuda Method allows you to have a greater chance to breed a shiny Pokemon by increasing your chances by approximately 83% (5/6).
2) Pokeradar Chaining allows to respectively encounter a certain Pokemon over and over until you chances of finding one is certain. Using this method is somewhat difficult but gradually boosts your chances for a shiny.
3) Chain Fishing/Consecutive Fishing is a fishing strategy used to repetitively encounter a Pokemon underwater. Finding narrow/enclosed spots among the water boosts your chances of getting a shiny after creating a long chain.
4) Receiving the shiny charm after completing the National Pokedex boosts the average chances by 300%, making it 1/1365.3.
5) Using GTS or trading with people is one of the easiest ways to receive one.
All these are ways to increase you chances of receiving a shiny Pokemon. But, there are some Pokemon in each game that remain shiny no matter what. These include:
1) Gible/Dratini with Haxorus in Pokemon Black/White 2
2) Shiny Beldum in OR/AS
But, there are many others depending on the game.
Hope I helped! :)