One strategy is to watch TV shows or Movies and listen closely to the actors.
Listening to music or radio on your phone or ipod while your doing daily activities is also helpful.
You can learn phrases you hear, and repeat them over and over.
Getting someone to correct your prounciation is another important part but you can also try to correct yourself by listening closely to your own voice.
If you are very serious about it there are people you can pay to teach you how to get rid of your accent or to acquire a different one. This would be the most effective way since these people have made a career out of figuring out how to help you.
well what I’m about to say is based on my experience and on what I’ve observed throughout my English learning journey, in many cases, this entirely depends on your own Native language, if you're Native language sounds a bit harsh and stiff to native English speakers then you'll face the same struggle they're facing when learning they're language, likewise if it's somehow easy for a native English speaker to speak in your own native language with minimum pronunciation mistakes, then you should find it to be quite easy for you to sound like a native English speaker, my second point is sometimes it's just simply an inherent ability (which was in my case), I’ve never really had any problems pronouncing words the way a native (American) English speaker would, in fact after a few years of learning English many people would mistake me for a native speaker.
Unless you are a spy, I would not work on getting rid of an accent. It's extremely difficult to do anyway, unless you have private lessons with a professional coach. Besides, there are Chinese Americans who were born here who still have an accent because they grew up with both languages.
I understand Melaminefree's point - it may not be beneficial to overly focus on your pronunciation. Unless you are planning to put yourself in the spotlight as an artist or some kind of leader, the most important thing it that you are understood, not that you are mistaken for a native speaker.
If you are concerned about your ability to be understood, I agree with Dorothy that finding a teacher is a great way to get this feedback and advice.
I am a professional teacher here in italki and could speak with you about your language goals. You can send me a message or check out my teacher profile: http://www.italki.com/teacher/493889