Sit back and keep your leg on
Just enjoy it and take baby steps
Bare back .. and don't get scared of long spots
make sure your heels are down and don't look down
have fun, don't jump before your horse, don't stand in you stirrups move forward with your horse. By standing you pushing your weight down
Look over the jump, not at the jump and always plan where your going to go to get to your next fence.
always keep your heels down! That's key to a pretty postion
Always be confident and trust your horse. I've been jumping for quite a while now and these are some tips: heels down(always), look forward, straight back, don't stare at the jump, and don't jump a jump that you're intimidated with especially if you're a beginner. And lastly ALWAYS HAVE FUN! I love jumping and I'm happy that you love it too. When you're skilled enough to show then try going to smaller shows first and then bigger local shows (don't go to a rated show for your first show).
I hope this helped!