Practice. and then more practice. Not just at the piano -- you can work on independent motion sitting at a desk, or waiting for the train, or whatever.
And don't get worried if you don't think you are making much progress! It can be remarkably difficult. In fact, most people never get complete independence. Just so long as you have enough.
I would suggest working with one finger at a time, though, at first, rather than combinations. Then when one at a time gets to be reasonably independent, start working combinations. Don't forget side to side as well as up and down...