First, basic safety. Make sure you don't wear and loose clothing and that you put on your safety goggles and hearing protection.
Next, make sure that you're using the correct blade for your project. As a general rule of thumb, if you're cutting with the grain, you want a ripping blade.
A crosscut blade will cut across the grain. Beyond the basic blades, look for specialty blades for different projects like clean cuts, trim, plywood, metal or concrete.
Before you cut, make sure that your blade is clean and that the teeth aren't dull or bent. Using a damaged blade can cause kickback which can injure you.
Make sure that you adjust your saw height according to the thickness of the wood you're cutting through. The blades should be set the depth of a saw tooth past the bottom of the wood.
When you start cutting, make sure that you stay straight and don't try to force the blade. If you feel it start to bind or hear it screeching, stop cutting, remove the saw and start the cut again.
Also, always watch where your power cord is so that it doesn't interfere with the saw and make sure that the wood is supported on both ends so that there isn't extra pressure on the blade.
Finally, always make sure that you let the blade stop spinning before you put down the saw. Easy tips to keep you safe while you're working with a circular saw. I'm Mrs. Fixit and it's just that simple!