A table saw, or a circular saw with a steady hand...
Drill
A sheet or two of 3/4" MDF
Wood glue
Clamps
Silicone sealant for the interior joints
Coarse-thread drywall screws to hold the box together while the glue sets
If you have a local lumberyard, they might be able to cut the boards for you. I wouldn't trust Lowe's or Home Depot to do it - they don't cut accurately enough 90% of the time.