First, the Shiny Charm was introduced in Black 2 and White 2. Don't waste time trying to get it in White.
Masuda Method is your best bet. Get two foreign Pokemon, and breed them for an increased chance of a shiny Pokemon (about a 5/8192 chance). If possible, shiny hunt in Black 2 and White 2 instead, or a newer generation, as those have the Shiny and Oval Charms, which White does not have. Keep at it though, you'll get a shiny eventually.
Hope I helped!