Remove the drawer you want to build a secret compartment behind. Measure the inside height, width and depth of the drawer compartment. The drawer compartment should have a closed top, bottom and sides for this type of compartment.
Measure the length of the drawer to determine the amount of space available behind the closed drawer for your hidden compartment. Subtract the drawer length from the drawer compartment depth.
Measure and mark a piece of 1-by-4 inch wood to make the false compartment back. It should fit closely inside the compartment and fill the compartment entirely. Cut the piece on the table saw. Cut one of the short sides at a 45-degree bevel, leaving one face of the false back the exact size of the inside back of the compartment.
Test fit the false back. Screw a small screw on the backside to use as a handle and slide the piece of wood all the way to the back of the compartment. Sand and trim the false back so that it slides into the compartment freely.
Cut a second piece of 1-by-4 the height of the compartment, but 3 inches narrower than the width. This will make the sides of the hidden box 1-1/2 inches from the sides of the compartment. Miter the ends of the hidden box back at a 45-degree angle sloping inward.
Subtract 1 inch from the depth of the space behind the drawer to allow for the thickness of the false back. Cut two sidepieces of 1-by-4 the height of the compartment and the depth you just calculated. Miter one end of each sidepiece at a 45-degree angle.
Assemble the secret box. Glue the flat ends of the sides of the hidden box to the back of false back, 1-1/2 inches from the ends of the false back. Make sure the mitered ends of the sides slope inward.
Glue the back piece of the hidden box to the mitered ends of the sides. Clamp or bungee cord the pieces together. Allow the pieces to dry overnight.
Measure the opening at the bottom of the hidden box. Cut a piece of 1-by-4 to fit in the bottom of the box and glue it into place. Allow the bottom to dry and then stain and varnish the entire assembly.
Fit the false back assembly into the back of the drawer compartment and slide the drawer in place.