here's how I skate, and it works very well:
from a standing position, I push off by angling one foot away from me and pushing off on that foot. Every subsequent stride is the same, only with alternating feet.
a more exxaggerated version of this is the T-Stop, where you have your weight on one foot (parallel with your shoulders) and the other foot perpindicular to that foot, to form a T (hence the name). Here's a picture, the guy is on streetskis, but the concept is the same.
If you feel you need extra balance, Try taking a hockey stick with you. It can give you some extra weight to counterbalance yourself, and if necessary, you can put some weight on it to keep from falling.
Like yakimushi said, keep your knees bent. it helps keep your balance. The goal is to keep your center of gravity. A T-stop position is a good place to start cause you can really feel your center, and it's easy to push off from there.
If you really want to get good at rollerblading, first get good at Ice Skating. The surface area you're skating on is a lot smaller and the rink is slippier, but once you can keep your balance on a pair of skates, rollerblading is easy by comparison. I started off ice skating, then moved onto roller hockey, and it was a breeze.
the best advice I can give is when you fall, just get right back up and try again. it takes practice but once you've got it, you don't lose it.