This question is a little broad, but I'll take a shot at answering it.
There are generally two ways that you can prevent chipping/tearout when cutting, sever the surface fibers in advance of your cut and support them during the cut.
Severing the fibers is pretty self-explanatory - instead of marking your cutline with a pencil use a marking knife to cut the surface of the wood. This doesn't have to be too deep.
Supporting the fibers during the cut can take a few different forms. The most common is a "zero-clearance" insert/guide on the side of the material the blade rotates out of. On a miter saw and table saw this is the table surface, on a circular saw or jigsaw this is the saw side.
You can also support the fibers with a sacrificial piece of wood, again on the side that the blade is coming out of. You can also get a similar effect with a piece of blue masking tape. Just be careful when removing the tape to pull it so that it doesn't lift the fibers.
In addition you should make sure that you're using a sharp, high-quality blade, and that you have appropriate RPM and feed rates.