Shiny hunting is arguably the most arduous task one can undertake in any core series Pokémon game. Normally, one has a 1 in 8,192 chance of encountering a shiny Pokémon in the wild. If you use the Masuda Method when breeding Pokémon, your chances rise to 1 in 1,366. The Shiny Charm further increases your chances of encountering shiny Pokémon, turning your chance of a wild shiny encounter to 1 in 2,730 and your chance of breeding a shiny via the Masuda Method to 1 in 1,024.
Based on these statistics, your best chance is to have the Shiny Charm and use the Masuda Method for breeding Pokémon, with a shiny chance of 1 in 1,024. Unfortunately, the Shiny Charm was introduced in Black and White 2, and doesn't exist in the prequels. Unless you own a copy of Black or White 2, your best chance is to use the Masuda Method, which gives you a 1 in 1,366 chance without the Shiny Charm.