What is the most effective method of discovering Shiny Pokemon in Pokemon black and white
There are multiple ways of doing this.
The Masuda Method
What you need for this is a Pokemon from another region (You can tell if it has a fre or jpn or something like that next to the Pokemon's name).
Get the shiny charm to make things a whole lot easier, as it increases the chance to encounter or hatch shinies.
You get it by completing the pokedex (You could go for a shiny hunt without the shiny charm, but it will probably take you more time to find the shiny you want).
Put both Pokemon in the daycare (The hatched Pokemon will be the same as the female).
Just keep hatching eggs until you get a shiny.
Somewhat less effective, but doesn't require any Pokemon from other regions.
Wild Pokemon could use moves wich prevent you from catching them.
Here you can read how to prepare for those:
Hope I helped!