Mark the cuts you'll make on the two sheets of 3/4 inch plywood using a pencil:
Two 24-inch by 48-inch pieces for the sides
One 24-inch by 40-inch piece for the top
Eight 3-inch by 24-inch pieces for drawer glide mounts
Eight 9-1/2-inch by 24-inch pieces for the drawer sides
Eight 9-1/2-inch by 30-1/2-inch for the drawer front and back pieces
Make the cuts with a table saw or circular saw.
Mark the four 23-1/2-inch by 31-1/4-inch cuts you'll need for the drawer bottoms on the 1/4-inch plywood using a pencil. Make the cuts using a table saw or circular saw.
Mark the cuts for the front frame on the 1-by-2 using a pencil:
Two 48-inch pieces
Two 26-inch pieces cut at 45 degrees on both ends
Five 33-inch pieces
Two 42-inch pieces cut at 45 degrees on both ends
Make the cuts using a miter saw.
Mark four 11-inch by 34-inch cuts in the 1-by-12 for the drawer fronts. Cut with a circular saw or table saw.
Attach the 3/4-inch plywood drawer glide mounts to the dresser sides with the 1-1/2 inch screws at 2 inches, 14 inches, 26 inches and 38 inches from the bottom edge. Put four or five screws into each glide mount. Attach the drawer glides to the mounts per the installation instructions for the glides.
Assemble the front frame by drilling two 1-inch holes into the ends of each of the 33-inch pieces and gluing 2-inch wooden pegs into the holes. Drill holes on the 48-inch pieces for the pegs to fit into. Clamp the pieces together while the glue dries.
Attach the front frame to the two sides of the dresser with the finish nails and wood glue.
Cut a 1/4-inch rabbet out of the 24-inch by 40-inch top piece of plywood all the way around the outer edges using a router with a 1/4-inch bit. Pre-drill screw holes then screw the top piece of plywood on to the sides and front frame.
Cut a 1/4-inch rabbet out of the angled 1-by-2 pieces and attach these to the rabbeted edges of the dresser top with glue. Clamp until dry.
Cut a 3/8-inch deep 1/4-inch dado into the inside of the sides, front and back pieces of the drawer. Assemble the sides and front of the drawers by drilling 1-1/4-inch screws through the sides into the front piece. Put glue on the edges of the 1/4-inch plywood drawer and slide it into the dadoes. Attach the back piece as you did the front. Repeat this process for the other drawers.
Attach the glides to the outside of the drawers per the glide installation instructions. Test the drawers in the frame to make sure all the pieces are lined up properly.
Attach the front faces to the drawers with six 1-1/4-inch screws through the back of the front drawer panel. The face should overhang an inch on top, bottom and sides of the drawer's front panel. Attach handles if you choose to have them. They aren't necessary but can give your dresser a lot of personality.
When finished installing the drawers, screw the 40-inch by 48-1/4-inch plywood back panel into place.
Sand the entire dresser with finish-grade sandpaper and belt sander or radial sander. Clean with a slightly damp cloth to remove any dust left from the sander.
Choose a finish for the dresser. You can use a polyurethane finish to give it a protective coating and a glossy sheen, a colored stain or a colorless finish that will enhance its natural beauty.
Wait for the finish to dry. Apply additional coats as needed.