Watch the serials, listen up to your favourite musics. Get a tutor who's got a nice English accent, talk and learn, make it a part of your daily routines. Anyway, nobody's perfect, and what makes it better is the more times you practise! 

There are usually two types that very common. American accent or British accent. It's up to you to choose what kind of accent that you want to learn deeply.
First, You can start with watching their movies (with english subtitle), film, video, anything as long as they native speaker or someone who really speak well in English. Listen their speaking, look their mouth, how they pronounce the sentence, word by word correctly. After that, imitate their accent by speak it aloud so you can hear how you speak it. Is it same or not?
Second, You can start with IPA (International Phonetic Alphabet) and English vowel sound or you can do this as a complement when you do the first one.
Next, you can determine your tutor/teacher to correct your word, or help you with pronounciation.
And I think the most important thing is practice. Try to use the correct spelling and pronounciation when you speak. It will train your tongue and your mouth. Don't fear to open your mouth. Make it clear. As Lenny said, make it a part of your daily routine. When you see a thing, do activities or will do other activities, try to think in English and speak it.
I am also a learner, hope it will help you :)

thank u ^_^