As many people here have already said, don't be afraid of Russian cases and of mistakes in general. Unlike the verb aspects which are quite difficult to master 100%, the cases are more accessible. Take one case and work with it, then add another and so on. Step by step :)

One of the most important tips: first of all, don't be afraid. Don't be afraid of cases. Usually, it is one of the hardest things for Russian learners. I can recommend to start from writing something in your notebook on italki. Step by step you'll understand the principles. It may take a lot of time, but you'll understand it at last, no doubt.

The second tip is simple. Listen to the native speakers. Talk with them. More you talk - faster you learn. Listening and speaking is the most important in language learning. Find language partner and try to speak, about anything.

Study the pertinent rules of grammar governing the use of cases.  Then practice, practice, and practice some more.  But I hope you will accept the following tip, which may be the most important I can come up with:  overcome any fear you may have regarding making mistakes.  If we didn't make mistakes, we wouldn't be human. 

Only one tip. Try, make mistakes, make lot of mistakes and one day you will be able to speak Russian without them.

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