I've got an American accent even though I'm not American (specifically I sound like I'm from California, even though I have a mixed background, born in Europe and lived in Hong Kong for the past 15 years.) I just spoke English everyday and watched a lot of movies and TV, but I guess it helped that I only speak English all day, everyday.
I'm no speech therapist but I am TESOL (Teaching English to Speakers of Other Languages) qualified. And I provide private tutoring at an affordable price, PM if you're interested. There's some tricks to getting any accent right I think. For example rolling r's (which is quite common in European languages) but is the most difficult for speakers of Asian languages.
I'm currently on summer vacation, but am teaching English until I start uni again. Private tutoring I do throughout the year.