Cut and Assemble the Frames
Add at least 2 inches to the combined length and width of your washer and dryer, and build two frames that size. Use 2 x 3s for one and 2 x 4s for the other. Then cut two supports to fit inside the frames, dividing the space roughly into thirds. Attach the parts with a pair of 3-inch deck screws at each butt joint, as shown.
Cut the Legs
The legs need to be tall enough to allow your baskets to fit between the frames. Measure the baskets, add about an inch to the height, and cut a 2 x 4 to that measurement. Cut another piece 6 inches longer, and spray it with paint-and-primer-in-one for a finished look. Once that dries, trace a notch on one end to fit over the 2 x 4 frame and a second notch on the other end to fit over the 2 x 3s. Cut the notches with a jigsaw, as shown. Repeat the process for the other three corners.
Make the Legs
Use 2½-inch deck screws to attach the shorter legs to the longer ones between the notches, creating legs for each corner with the painted portion facing inside the pedestal. Add construction adhesive to the longer notch and place the leg in a corner so it fits over the 2 x 4 frame. Drill pilot holes through the leg, then attach it to the frame with 2½-inch deck screws, as shown. Repeat with the remaining legs. Repeat the process for the other three corners.
Attach the Lower Shelf
Using a circular saw and a straightedge, cut the melamine panel to the dimensions of the lower frame. Screw two scraps of 2 x 4 together and use them to mark notches at the corners of the panel so that it will fit around the legs. Cut the notches with a jigsaw. Drop the panel in place, then fasten it to the frame with 2-inch finish nails every few inches along both sides and the back, as shown.
Add the Upper Frame
Apply construction adhesive to the notches at the tops of the legs. Then fit the 2 x 3 frame in place, as shown. Screw through the outside of the frame and into the legs with 2½-inch deck screws.
Prep the Parts
Measure the length and width of each side, then use a circular saw to cut beadboard pieces to fit. Cut two pieces for the back the same way, then prime and paint the beadboard. Let it dry.
Attach the Beadboard
Use clamps to hold a piece of beadboard on the back, flush with the top of the frame and a corner, so the pattern faces in. Attach the panel with 1¼-inch deck screws every few inches. Butt the second back panel next to the first and attach it the same way. Repeat the process for the sides with the beads facing out, as shown.
Make the Stiles
Cut two 1 x 4s and four 1 x 5s to the height of the pedestal. Position a 1 x 4 along a side with its edge flush with the front corner, and fasten it with nails. Next, make a corner board by nailing a 1 x 5 on the front face of the pedestal so it covers the flush edge of the 1×4. Repeat the process for the other front corner, then add a 1 x 5 to the back edge of both sides.
Add the Rails
Mark each of the 1 x 4 side rails to fit between the stiles, as shown. Cut them to length and attach them with nails. Repeat the process for the two front rails and install the lower one so it covers the edge of the melamine panel. The exposed frame under the lower rail will be hidden with molding in the next step.
Cut the Plywood
Place the plywood top on the pedestal and scribe cutlines using the face of the trim, as shown. Remove the top and cut it with a circular saw. Drive 1¼-inch deck screws through the plywood and into the upper frame.
Mark the Base Molding
Hold a strip of base molding across the front of the pedestal, overlapping both ends. Mark the locations of the 45-degrees outside miters on the back side of each end and cut them with the miter saw. Attach the piece with nails. Cut the two side pieces with a miter at the front end and a straight cut at the back. Nail them in place. Repeat the process for the shoe molding.
Add the Panel Molding
Mark, miter, and install the front and side pieces of panel molding flush with the top of the plywood. Fill all joints, nail holes, and screw holes with paintable caulk. Prime the plywood top, then paint the pedestal.