I find the best way is to consume media with the particular dialect you'd like to acquire. Movies, music, shows, etc, and try to find people who use it. Memorizing short speeches or phrases helps you get used to what sounds are native to the dialect, and longer monologues should help with what words are more common in that dialect as well.
One caveat with movies and what not is the writers and actors usually do a good job of emulating it, but it's not always exact. Specific types of media like documentaries, reality shows, and news casts should help you hear people who really use the dialect rather than those who are just acting.