I can tell you when I started hunting out of a climber twenty years ago I was shakey. And that was after I use to teach rappelling (sliding down a rope from a tower and a helicopter). Some of the things that helped me over the years;

1) Invest in the best equipment (climber or hang on stand) that you can afford. Confidence in the quality of equipment goes a long way for me. I use to use home made climbers that would bust a weld when I was in a tree...not fun.

2) Follow manufacturer's guidelines for use; weight limit, size of tree, etc...

3) Use a full body harness. For me, having four points hookup makes me feel better.

4) Don't look straight down if you can help it. I use to have a problem with that, until I got comfortablewith it. Even after rappelling for many years, there is a difference between looking straight down off of a tower and looking straight down off of a small platform.

5) Gradually increase your height. When I first started, I didn't want to get ten feet off of the ground. Now I will go thirty without hesitation. It took me years to get to that point.

6) Practice climbing...a lot. This is the only way you can gain confidence in your equipment and abilities.

Good luck!