While solid wood box lids and doors are easy to make, they do have one really bad habit - they tend to cup or twist. Plywood doors and box lids, on the other hand, stay flat as a pancake, but they also have a bad characteristic - they have ugly edges. You can glue edging to the plywood, but often that edging can be distracting, and it often breaks loose with use. But there is a solution that solves all these problems: making your own hardwood plywood lid or door.
Start by deciding how big the lid (the piece I'm building in this case as an example) needs to be. While you can trim and fit this sort of piece, there are limitations. Do the math and cut your parts. You need a plywood core and hardwood trim pieces. My lid is made from walnut trim strips and veneer, with a 1/4" mahogany plywood core. I trimmed the hardwood strips on the table saw to be 1/4" thick and 1/2" wide.
Next, carefully miter the trim strips to fit snugly around the perimeter of the plywood core. I used masking tape and white glue to attach the strips to the core (Photo 1). Allow the glue to cure and then sand the strips so that they align perfectly with the face of the plywood core. I did this with a random orbit sander and 80-grit paper. (You don't need to go any finer with your sandpaper than that.)
Now that the core-blank is prepared, you need to select your veneer. One huge advantage to this technique is that you can totally control the figure and pattern of the wood grain by selecting the section of veneer that is most pleasing to you. You can, of course, secure the veneer to the core by any of the traditional methods of gluing and clamping veneer to a substrate. Because my lid was small enough, I chose one of the fastest and easiest techniques I know for this task. Simply brush white (or yellow) wood glue to both the substrate and the veneer in a thin layer and wait for it to dry completely (Photo 2). Then adjust a regular household clothes iron to its highest setting. Place the veneer and substrate (the core-blank, in this case) glued face to glued face and "iron" them together - pushing down hard on the iron as you do it (Photo 3). This activates the glue and bonds the two surfaces instantly. (They better be properly aligned at the start of this process, because once they get hot, there is no adjusting the veneer's location.) Veneer both sides of the core-blank. I trimmed away the excess veneer with a sharp utility knife and then sanded the edges smooth. That is it: you are done.
Some woodworkers will call this "baking in" an edge. Done right, it is nearly impossible to see the transition between the veneer and the hardwood trim. The lid is strong, durable and will stay dead flat. You can attach hinges through the veneer into the hardwood strips very securely. As you can imagine, it is possible to shape and treat the edges within the width of the hardwood trim.
All in all, it is a very useful technique to add to your arsenal of woodworking tricks.