One very common problem in beginning vaulters, and sometimes in more experienced ones, is leaning too far forward on the board on the punch. If you've had this problem, you'd notice that it is very scary and very difficult to vault correctly. It causes you to lose height and power on the pre-flight, and you are in danger of smashing your face into the vault.
There are a few drills you can do to fix this problem, all of which are based on the same technique. The goal is to punch on the board with your torso vertical (perpendicular to the ground) and with your feet in front of you. This will give you the height you need and the proper body angle for your pre-flight.
Begin on the floor, preferably in front of a line on the ground. Take a one step hurdle with an arm circle and do a punch jump as if you were jumping on a board. Punch a few inches in front of the line. Ideally, you should jump with your feet in front of you, your chest back, and with a tight body. If this is done correctly, you should bounce backwards a little and land behind the line.
When you get used to that drill, begin doing the same drill but onto a board. Take one or two running steps into the hurdle. Bounce with your feet in front of you and you should bounce straight up and land back down on the board. Take some time and get used to the feeling of controlling the punch so that you don't bounce wildly off the board, but instead land straight back down on the board.
The next step is to take a half or full run to the board and horse, with the board at or less than your usual setting. Do the arm circle and hurdle, and punch off the board so that you do a tuck jump onto the horse. When that becomes easier, get more power into the approach and try punching onto the horse with a straight body, as illustrated in the animation. (For the first time doing this drill, have a spotter at the horse until you become comfortable with it.)
Remember, this is how you want to have your body when you punch off the board when you do forward vaults, such as handsprings or half-ons. With enough practice, this position will become second nature and you will notice your vaults becoming easier and more powerful.
For more, also see Vault: The Approach.