A drawer is nothing more than an open box. It can fit flush with the front of a cabinet or it can be made with a false front, a board that overlaps part of the cabinet front, concealing the gap between the cabinet and the drawer sides. A flush drawer must be more precisely made because this gap remains visible.
Plan drawers on graph paper with the rest of the cabinet. Design the back and bottom to fit into 1/4-inch grooves cut into the sides. In calculating the size of the front and bottom, allow for the thickness of the drawer sides minus the depth of the grooves the front and the bottom will fit into. Also allow room for wooden runners or metal slides. A standard slide takes up 1/2 inch.
On false-front drawers, butt the front between the sides and add a false front that is 3/8-inch larger on each side than the drawer opening. On flush-front drawers, cut rabbets into the drawer front to fit it over the edges of the drawer sides.
Make the false front (or the actual front in a flush drawer) of the same material as the rest of the cabinet. You can use cheaper plywood for the rest-1/2 inch for the sides and invisible front; 1/4 inch for the back and bottom.
Cut all the pieces; cut the grooves and rabbets and test their fit. Then assemble and glue the drawer. If needed, reinforce the joints with brads driven through the drawer sides. Clamp the drawer until the glue is dry. Attach a false front by driving screws from the rear.
If you use metal slides (available at hardware stores and home centers), follow the manufacturer’s directions to install them. Or make your own wooden runners. Simply glue and nail strips of wood along the sides of the drawers and on the insides of the cabinet so that the strips on the drawer sides rest on the strips on the cabinet at the proper height. Also nail a strip of wood, or kicker, to the cabinet above each drawer side to keep the drawer from tipping as it is pulled out. Be precise in positioning runners or slides; otherwise, the drawer will jam.