Plane all boards to be used during drawer construction to the same thickness. Pay particular attention to the pieces of wood that will join each other. Matching thickness at the joints eases the task of creating mortise and tenon with a good fit. A tenon fits properly into a mortise when light tapping with a hammer is required to insert the tenon.
Cut a mortise, which is a square or rectangular hole, with a router, drill press or mortise machine. According to Tom Hintz of NewWoodworker.com, the most important consideration, regardless of the tool used, is to center the mortise in the wood. Hintz states that cutting from both sides of the wood simplifies the task of centering the mortise. Cut the mortise slightly deeper than the length of the tenon.
Shape the tenon with a table saw, router table or arm saw. Just like the mortise, the tenon must be perfectly centered in the wood. The width of the tenon should be just tight enough to fit into the mortise when tapped lightly with a hammer.
Measure the width of the drawer panel. Cut a length of dowel stick or wooden skewer to this dimension. This is your peg. Using a drill with a bit slightly smaller than the peg, drill a hole through the center of the mortise and tenon joint. Apply glue to the inside of the hole. Tap the peg into the hole. A pegged mortise and tenon joint is extremely strong.