there are lots of great suggestions here. I agree that I would use a longer ruler, and you need to have a good flat cutting surface that is the right height for you. A table that is too high is hard to apply the proper pressure. So a dining room table may be better than a kitchen counter, for example.
When you are cutting place the cutting edge of your ruler directly in front of your cutting hand. You will be able to apply better pressure with your rotary cutter if you are properly centered in front of your work, and that means the cutting wrist should be going straight forward, the blade should be perpendicular to the table and rolling right along the edge of the ruler, not at any kind of an angle to the ruler or table other than straight up and down.
The little discs you can put on the underside of your ruler to keep them from slipping can be purchased at your LQS or online. In a pinch, you can use little squares of sandpaper that you place on the underside of your ruler with double stick tape.
When you have placed your ruler and you are about to make the cut, take your "ruler hand" and lay it down along the edge of the ruler, so that the inner aspect of your pinky is right along the ruler's edge (on the side that is not the cutting side, obviously!). This will help to stablize the ruler and keep it from sliding and it will be much less pressure on your wrists than if you are using the ends of your fingers to hold the ruler. Most demonstrations of rotary cutting show the person with her hand like a spider on the top of the ruler. I'm suggesting that you put your hand flat on the ruler, with your pinky along the non-cutting edge. *Make sure all your other fingers (especially your thumb) are within the margin of the ruler and are not in the path of the cutter!* As you move the rotary cutter up the length of the ruler, you will have to move your hand up one or two times as well, so slide it up or walk it up carefully. this will prevent the end of the ruler from pulling away from your rotary cutter as you get further away from your body.
I would also suggest spray starching your fabrics before you cut (Mary Ellen's Best Press, available in your local quilt shop or on line is wonderful, but any will do) and once you have some confidence in your ability, it may be advisable to invest in one of the cutting machines (such as the Accucut GO) which is very accurate and it will take a lot of the pressure off your wrists. you will turn a crank to feed fabrics under a die cutter/roller system rather than using a rotary cutter.
Hope this helps. there are lots of great suggestions for you here!
Lisa