Choice of screw
The length of screw should ideally be two to three times the thickness of the wood being secured. Hold the two pieces of wood together, using a suitable method. This will depend on the circumstances - small items may be held in position on your workbench, others may require the use of a clamp.
Mark the position for the screw with a pencil. Drill a pilot hole, a little narrower than the thinnest part of the screw, through the top piece of wood and into the bottom piece. The depth of this pilot hole should be roughly the same as the length of the screw.
Ideally, you should now make the hole in the upper piece of wood larger, to match the diameter of the shank. This is more important in hardwoods and quality joinery.
Countersink or recesss
If you are using countersunk screws, you should now use a countersink borer - a hand tool or power-drill attachment - which creates a recess in the surface to accommodate the screw.
If you have a lot of work to do, you may want to invest in a set of special drill bits which are shaped to do all these functions in one go.
Place the screw in the hole and fasten with the correct type of screwdriver. The blade of the driver should be the same width and gauge as the slot on the screw - using the wrong size will cause the screwdriver to slip and the screw to become damaged.