A rotary cutter is a razor blade but without the guard. Do a quick image search of 'rotary cutter injuries'. I haven't included any of the graphic pictures in this post, they are not pleasant! Knowing how to use a rotary cutter safely will not only save your fingers but will also help you cut your fabric quickly and more accurately making your projects go together more easily.
Find a rotary cutter that is comfortable for you to grip. There are lots of makes out there, do your research, ask other quilters and test some out if possible. You don't need a special cutter if you are left handed - the blade can be carefully swapped to the other side.
It is much safer to stand when you are rotary cutting. If you can't stand easily, make sure you find a rotary cutter that is designed for use sitting down, such as a Martelli rotary cutter.
Use a quilting ruler, they are thicker than a normal ruler, and will help you measure the fabric you are cutting.
Standing straight on, hold your quilting ruler securely with your non-dominant hand. You can move your finger tips up the ruler to keep it steady as you cut along your fabric.
Expose the blade of the rotary cutter and butt it up against the edge of the ruler.
Press the blade down on the fabric and move the rotary cutter away from you along the fabric keeping the pressure constant. NEVER cut towards or across your body.
Make the blade safe as soon as you lift it away from the mat...EVERY time you lift it away from the mat. Get into the habit.
Before you move the ruler, move the fabric away. If some of the fabric has not cut you can go back over it with the rotary cutter. This might happen if you have an old blade or mat, have run over pins and damaged the blade or have not used constant pressure.
Rotary cutters are an incredibly useful tool for quilters but, they are also incredibly dangerous. If you leave an open blade on a cutting mat not only you could get hurt, the people (including fur people) you live with could get hurt. If you leave the blade open at a workshop your fellow quilters could get hurt. Also, you will get blood on your fabric!