Here's the way I learn new accents. Bear with me.

I have a hard time learning from people with the accent. Rather, it's easier for me to learn from people who imitates it. Weird.

I know what the American accent (let's say, the 'regular' one, not the Southern one) sounds like. I couldn't talk like that (or at least, I didn't know how close I was). British accent, easy for me, because I learned from someone who could mimic it.

Cue that Monty Python sketch where they're speaking like Americans (it's the Philosophy dinner, I think). Bam, clicked right in.

Charlize Theron mentioned in an "Inside the Actor's Studio" that she solved her accent by "overdoing" the accent she wanted to sound like