You definitely shouldn't be gripping the horse with your legs. Someone on here said something to the effect of letting your leg wrap around the horse like a wet cloth (Heather or Sarah, perhaps). I think having this leg position is difficult for a beginner to actually do, and it comes with a lot of practice.
In the meantime, you could just try your best to keep your legs relaxed, and let your weight settle into your heels. However, don't ram your heels down; this is very counterproductive. Try to gently roll your thighs inward as if you were trying to touch the sides of your kneecaps together. But don't force your thighs to roll in too strongly or you'll end up gripping tightly, which will ruin your position and signal the horse to slow down (I think that's what the horse will think you want...someone else will know for sure
It also helps to make sure you're sitting in the saddle correctly. You should be sitting in the lowest part of the saddle, which is in between the center of the saddle and the pommel (you'll be sitting rather close to the pommel). When you're in this position, take your feet out of the stirrups, straighten your legs, and bring them out away from the horse. That's what I do to make sure I'm sitting in the saddle snuggly.
Moving your horse forward is done with the inside of your calf muscles. The amount of pressure used and the frequency depends on the horse. Start out lightly and get firmer as necessary. Don't tire yourself squeezing the life out of the horse though; back up your leg aids with a light tap from the crop if need be. Again, when you're not working your horse, your legs should be wrapped lightly around his barrel.
Hope I've helped!
[This message has been edited by CLAUDIA (edited 31 December 1999).]