I agree with what everyone has said here: there's no magic bullet for doing a proof. However, one "strategy" I would suggest is to keep trying. Persistence is the key to solving math problems. For any given proof, there are many, many ways to get to that magic QED statement. And there are many MORE ways to get to a dead end. Here are a few suggestions:
1. Draw the pictures, beginning picture and ending picture, if possible. Some minds work with graphics better than variables (I also like looking at pictures better than reading words, and I write for a living).
2. Divide and conquer. This means, break it up into tiny steps in your head and on paper. Write everything that occurs to you, based on the theorems and math facts you know, as to how you can morph the starting point into the ending point. It's perfectly OK if you take 20 steps to do a proof and the answer in the book has only three, as long as each of your steps is logical. There are many paths to the right answer. I can't say that enough. The Chinese (or people from some country) have a proverb: A journey of a thousand miles (probably kilometers, if it's from China) begins with a single step. And some of those steps, in solving geometry proofs, may actually take you AWAY from the solution: sometimes you have to take a step back before you can go forward the rest of the way.
3. Step away from it for a day or sleep on it, with the picture in your head. The brain is an amazing organ, and sometimes it keeps working on a problem, even when you don't have a pencil in your hand.
4. Don't ever give up. Your teacher, I hope with all my heart, knows that there's an answer to every problem he or she gives you, so if you run into a dead end and follow an approach that took you basically nowhere, throw it out, and try something else. You can find ideas for how to solve it in your book (if it's a good one), on the Internet, from talking to others, etc. Be resourceful, and be very patient with yourself. I hope your teacher is also patient with you. Some of this stuff is pretty hard.
