Your story pretty much sounds like everyone that's ever started snowboarding.
At this point, there's not much advice to give besides doing it more often.
Most of newer riders and a couple of my friends that started out snowboarding had the same problems. I'm not very good myself but I did notice that they were all not bending their legs and generally looked very tense.
So bend your legs and keep a good posture! Don't lean over and when you start acquainting yourself with your balance, keep your hands (especially your back hand) at your side or over your tail. I see so many retards flying down the mountain with one arm sticking out and they're leaning over just about ready to wipe out.