Reddit reviews Joan Wulff's New Fly-Casting Techniques

Fishing is the best practice. If you don't have a mentor, invest in a couple fishing trips with good guides. You'll learn exponentially faster with a mentor or guide than you ever could on your own. Find a guide that's familiar with your home waters that you think you will fish the most. Learning a stream and how to fish it is half the battle.

I would also recommend Joan Wulff's book, New Fly Casting Techniques. She has a gift for simplifying the fly cast in easy mechanical terms and her book includes exercises and tips for improving your casting accuracy and distance.