Cut the plywood with a circular saw based on the desired dimensions of the front, back and sides of your drawers.
Glue and nail the sides first. The front and back must be glued and nailed between the sides. If you use finish nails instead of a nail gun, predrill holes to avoid splitting the plywood.
Measure the top and bottom dimensions needed for the drawer, then cut from the plywood.
Glue and then nail the drawer top and bottom pieces. Use a carpenter’s square to ensure the drawer box is square.
Cut the sides of the cradle to the same dimensions as the sides of your drawer. If you decide to stack more than one drawer, build one single cradle in which the drawers share the cradle sides and base.
Draw a horizontal screw line across the drawer sides at its center. Do the same for the cradle sides.
Take the drawer slides and pull them apart so you have the drawer member and cradle member.
Center the screw holes of the slides over the screw line and drill in place. Slip the slides of the cradle with the drawer, so that you have the cradle sides now attached to the sides of your drawer.
Flip the drawer upside down. Measure the dimensions needed for the cradle cover and base and cut the plywood accordingly.
Attach the cradle base and cover to the cradle sides with screws only. The drawer should now be self-contained within the cradle.
Lay the plastic floor covering on the floor and carefully remove the drywall with a reciprocating saw according to the size of the cradle. Slide the cradle into the wall.
Cut the drawer face to width. But when you cut the length, ensure the drawer is flush with the outside of the cabinet -- leaving a ¼-inch gap between the neighboring faces or each drawer.
Use a nail gun to attach the drawer face to the the drawer body. Then, screw in the drawer pulls.
Attach wood trim to the border to hide the dry wall from where it was cut. Ensure that once the wood trim is nailed in place, it does not interfere with the pulling of the drawers.