Measure the existing drawers to determine the proper drawer dimensions. Determine the type of drawer track. (Older cabinets use wooden rails where the drawer sides slide on wooden rails).
To make each drawer face, use the measurements of the existing drawer openings and add 1/2" to the height and width. Cut the 1/2" wood stock to those adjusted measurements.
To make the drawer sides, rip 1/2" plywood to the depth of the existing drawer depth. Cut the ½" plywood to length at the full dimensions of the drawer box. You'll want to create two identically sized pieces for the sides, and two to create the front and back.
At the table saw, you'll need to cut a dado groove into the sides of the drawer for the drawer. Place a dado blade into a table saw with the dado thickness set to 1/4". Set the table saw fence so that the dado cut is 1/4" from the bottom edge of the drawer sides. Run the drawer sides through the dado cut on all four sides of the drawer bottom (Images 1 and 2).
Place a side piece and a front (or back) piece into the dovetail jig at a 90-degree angle (Image 1) and slightly offset from each other— by the distance specified by the jig (typically 1/2"). Using a router with the dovetail bit, place it into the jig to cut the dovetail pattern on both boards at the same time to create the dovetail joint (Image 2).
To make the drawer bottom, cut a 1/4" piece of plywood to match the size of the drawer inside dimensions. Be sure to add 1/2" for the combined depths of the dado cuts of the assembled drawer sides.
To assemble the drawer box, first apply a small amount of glue to each of the dovetail joints. (Avoid getting glue into the dado grooves.) Position the first two pieces with the dovetails aligned and tap the dovetail joints together at the corners of one side (Image 1). Insert the 1/4" drawer bottom panel into the dado grooves (Image 2). Tap in the last side in place, seating it securlely with the dovetail joints.
To apply the drawer face, first prime and paint the drawer face and allow to dry. Attach the drawer face onto the assembled drawer box using short screws
Slide the completed drawers into the cabinet.
Add drawer pulls or handles as required.