The top is 3/4" plywood that I painted blue. I like the contrast the alternating layers of ply make when painted

Cherry plywood and amber shellac 

The bottom is 1/4" ply and is also painted. I may skip that in future versions - the blue is a bit much

Simple mitered construction 

See the attached Sketchup (thanks Sean!) for the details.

This is some 1/2" scrap cherry plywood I had laying around. I cut some grooves in for a bottom and lid 1/4" wide, 1/4" deep, and 1/4" from each edge.I was going to make the lid inset, but decided to make a rabbet on the top instead of the groove. 

Cleaning up the rabbet with a router plane

I cut miters and pre-finish the inside with amber shellac. This it to make sure the inside of the box gets a good looking finish as it's very difficult after assembly, and it makes cleaning up squeeze-out easy

I painted the 1/4" plywood bottom blue to match the top

Then I put everything together and used painters tape as clamps. The only "problem" with plywood is the miters have to be perfect. Sanding/plaining/or rounding over isn't possible like it is with solid wood. I used my miter sled

Here I cut the lid. It's just 3/4" pre-primed plywood. Because the rabbet is only 1/2" deep, it sticks up 1/4". 

I use the same blue to paint the lid    

Perfect fit! Now time for some amber shellac