The first thing to do is start with the right bit. Inexpensive standard twist bits are typically ground to a shallow angle. That can allow the bit to wander on entry and blow out wood fibers on exit except for holes under the size of 1/8". For holes sized from 1/8" to 1/2", use a brad- point bit (pic 1). The center point of a brad-point bit prevents wandering on entry, while the sharp outer spurs shear the wood for far less tear-out (pic 2). If you need a hole larger than 1/2", use a Forstner bit. It has a center guiding point like the brad-point and cuts very clean holes. To prevent tear-out place a piece of scrap wood behind hole. Regardless to the choice of bit any time you punch through wood, unsupported wood fibers on the back of the work piece can tear out. The backing board traps the wood fibers, preventing the bit from pushing out the last splinters. When using a drill press, slide a scrap beneath the work piece; for handheld drilling, clamp the backer in place (pic 3). Masking tape on the front will help prevent splintering at the entry point, but don't forget to do it before you mark your layout lines (pic 4).