The process is similar accent reduction. In order to successfully adopt an American dialect or a foreign dialect you have to be able to identify what's different about it and how to execute it. The reason why I can pick up accents/dialects quickly is because I already have a system in place for what Neutral American should be. In order to then switch to Cockney, British, Southern, etc it's simply a matter of identifying which of these sounds change for that particular accent and then drilling those changes so they become easy to execute. If you have the time and want to achieve the highest level of an accent, you'd drill until you can improvize while holding the accent without making the accent itself seem like you're putting on a character. You should be able to still feel like yourself even though you're changing how you speak. It's when you put the character's point of view, physical impediments, vocal patterns and dialect together that you get the final product.