How to reduce my russian accent?

Do you have some tips on how a person could reduce his accent? Cause Because when I watch some films, where people try to speak Russian without practice, their accent sounds really terrible. So I guess that my accent in English sounds weird too. So feel free to give me some recommendations. Thanks.

Tips:

* Find a short bit of audio, ideally just a sentence. Listen and repeat, trying to imitate as best you can. Listen carefully so that you notice all the subtle differences in sound.

* Listen a lot to the language so you soak up the natural rythm and sounds.

* Take a lesson, or use a language exchange to get feedback from a native speaker.

* Record your voice on Vocaroo or Soundcloud and post a link here so we can give you feedback.

* Remember intonation and pronunciation are important, not just accent.

* There's no need to lose your Russian accent completely, you should retain your identity. We English speakers all have our own regional accents.

* If people can easily understand you and don't find you unpleasant to listen to, then your accent is already good enough.

I think the best way is just to ask a native speaker. Ask them to be absolutely honest with you, to correct you on every teeny tiny mistake you make, because often someone's English is really really good, only they don't realise that they have a typical pronunciation.

I once told a Polish friend of mine that he tends  to pronounce the letter 'h' really strongly, like the way they pronounce a 'g' in Dutch or a 'ch' in German, or simply the 'х' in Russian (A lot of speakers of Slavic language do this). He had never heard it before, and never knew he did that. After that, he paid attention to it and solved the problem.  It's not that he couldn't do it, he had just never known...

Only watching movies or listening to audio may not be enough. I once read this research on Chinese people and their difficulties recognising and reproducing the difference between 'l' and 'r' in English. 

They took some Chinese people and showed them on a computer screen the words lock and rock, with the instruction to pronounce them. As you would expect, they pronounced them exactly the same. Then they had them listen to the two different words, and make them say the words too. After a lot of trying they still pronounced them the same.

Then, they made them pronounce the words, but every time they did, the screen on which they read the word, would immediately turn green if the word was pronounced correctly, and red if it wasn't. It was only after a few tries, that they started to recognise the difference, and started being able to reproduce it.