I made my Cajon with leftover flooring. The size of the boards is 6 inch x 5/8. I got them in random lengths.The top is a birch 1/8 inch plywood from the local lumber store. One side is glued and one side is screwed. It also has a snare wire inside to make a snare drum sound. This one is adjustable. The other side sounds like a bongo/conga drum.
Step 1: Start Cutting and Clamping!
So to start I cut the edges flat. I Picked a size that worked to find a shape i wanted. I then mitered the corners so the plywood edge would not be seen. After being cut the wood is glued and clamped for a specified time to set the glue. After that unclamp and clean the glue off. Sand the edges to make a flat surface.
If you install a snare for the sound you may want to screw one side on to service the snare wires. Glue and screw your top and bottom on. Sand the edges smooth. You can then finish the top with Clear Poly, Oil, or paint your cajon.