[somehnreader]

I came to England in my 20s and am now often complimented on my pronunciation:

Try to over exaggerate the way natives speak your target language, almost as if you were mocking them (Do it by yourself first, not in a conversation as that might make them punch you).

Watch QI and try to speak like Stephen Fry does, or if you want a US accent do the same with American shows. After a while you get the hang of it and you speak more natural.

I am in no way able to trick English people into thinking that I am one of them, but other foreigners always assume I am English, to Americans I just sound British.