Cut a front, back and two side panels for your drawer. Wood thickness and size will depend on the drawer's size and how sturdy you'd like it to be. A cabinet drawer, for instance, might have side planks measuring 3/4 inch by 4 inches.
Create a dado across the bottom of each of the four side panels using a Dremel tool. The dado should sit about 1/4 inch from the bottom edge of each panel. Depth depends on the dimensions of each plank, but a 3/8-inch deep dado works well for about a 3/4- to 1-inch thick panel.
Carve out a box joint on either side of each side panel. The exact measurement depends on the size of your drawer. Create two to four notches, depending on the drawer size, using a handsaw.
Cut a plank of plywood or solid wood for the drawer's bottom panel based on your desired measurements and desired thickness.
Fit the sides around the panel to test for a secure fit, making sure to interlock the corner joints snugly. Glue the pieces in place.
Drive several nails into each drawer corner, making sure they're shorter than the thickness of the wood and don't stick out the other side.
Attach a handle or drawer pull on the drawer face, if desired. Mark your desired spot, and pre-drill holes before installing the hardware per the manufacturer's instructions.
Install any additional glides or hardware necessary, depending on the drawer's intended function.