1. Practice the squat!! The squat is so essential to the backward motion of the skill. You've probably heard it many times, but it should be as if you're sitting in a chair. You need to get a good bend in the legs and sit back. The backwards motion starts here!!
2. Get a strong arm swing. You should practice without the arm swing, too, so you can figure out how to push hard with your legs to make the handspring. But once you know you have that down, the arm swing will get you some good momentum. You should, of course, combine this with the push from your legs as you extend your legs and spring off those toes.
3. As you begin the first phase of the handspring, really open your shoulder angle (note: that does not mean that you should throw your head back!) and open your hips so that you find that nice tight arch position over the top.
4. Over the top of the skill, your arms need to be tight at your ears with your head staying in place, chin tucked in slightly. Of course, straight legs, tight core, and pointed toes. At this point, you can start spotting for the hand placement with your eyes.
5. Immediately after your hands hit the floor, you need to block as hard as you can off of your shoulders. Do not bend your arms and push off - the block should happen all with shoulder power, and of course with straight arms (not locked, but straight) and your fingers slightly turned in to prevent injury to the elbows.
6. Now you're ready for the turnover. What you're going to do now is to snap your legs down towards the ground for the rebound. You can do snap-down drills by kicking up into a handstand on a panel mat and snapping your feet down, first controlling the landing by bending the knees and landing with a hollow chest, then trying the same thing with a high rebound once your feet hit the floor.
7. During the rebound, your knees should not bend. Similar to your hands hitting the ground in the handspring, you do not want to lock the knees but they should be straight. The rebound really comes from pushing off the toes as hard as you can. After you get a great rebound, you can start working on sets for a back tuck!
8. Coming down from the rebound, bend the knees slightly to control the landing and extend your hands our in front of you for balance. Keeping a tight body throughout the skill and the rebound is going to help you to stick the landing.
Following these basic tips you should have a pretty nice back handspring :) Remember to stretch out your back with bridges and back walkovers before jumping right into the handspring! Happy flipping!