A number of years ago the first thing an instructor said to me was, "Tell me something. Do you ever breath?" I had to laugh but it made a big impression and made me realize how important breathing and relaxing is.
As you get more experience it will be easier to relax and relaxing will certainly help your horse too. Something that helps me is to relax first the shoulders, arms, hands, back, legs. When you think about it, it's amazing how tense one can be and not realize it until you start relaxing piece by piece. (This also works for going to sleep at night, or driving, or ?....)
Another thing to keep in mind is that it takes time to learn to sit a horse well. Don't be hard on yourself. You are going to have good lessons and tougher ones. Don't be afraid to ask the instructor to stop and further explain something if you are not getting what he/she is asking you to do.
Wishing you the best!
If you ever find yourself in a fair fight, it's because your tactics suck. ~ Marine 1SGT J. Reifinger