We know this from the science of linguistics, but we also know this from experience. Think about it for a moment. People sound like where they’re from, sure (usually). But they also sound like the group they feel like they belong to. It’s why kids almost always grow up sounding like their peers, not their parents. Think about kids who move from one place to another and how quickly their accents change to fit in. Variation in accents isn’t just about where you’re from, it’s about who you are.
Does this mean you need to become American to sound like an American, English to sound like you're English, and so on? Abandon your own identity?
No, it doesn’t.
It might work, but it’s an awfully drastic thing to do, and it’s not necessary!
It does mean that you need to imagine what it feels like to be from the place and culture, to see the world around you from that perspective, to discover and absorb some common cultural referents. It means that the deeper you take all that into your bones and craft a genuine and specific sense of an that identity, the better your accent will be (and the faster you’ll see results).
This is an acting job—one you probably already know how to do. And just like with any character you play, this work doesn’t have to (shouldn’t!) replace your own deepest self, your own identity. It should be an optional self, a mode you can switch into.
So, how do you do this? By using your most essential ability as an actor. Engage your imagination. Feed yourself with rich material to get your imagination excited to get to work on building an alternate self.
If you happen to be working on a "General" American accent, I’d love to share with you some suggestions for movies, books, music, TV shows, and art that will help you start getting some American culture and identity into your bones (and mouth!). If you sign up for my "General" American 101 webinar I'll make sure to get them to you, along with tons of other goodies!