Plyometric boxes are a fantastic workout tool and are common sight in Crossfit Gyms. They're quite expensive to purchase but much cheaper to make, and they aren't overly difficult to construct.
At my gym we've got a number of different boxes, several each of 12", 18", 20" and 24" heights. One of the other members told me that she wanted to progress past the 12" box she was using, but wasn't quite ready to move to the 18" box, and asked if I could make her a 15" to bridge the gap. For that reason these instructions will be based on a 15" box, but once you understand the basic construction you can easily make plans for any size that you'd like.
I'm also going to go into depth regarding setting up a workflow that lends itself to churning out multiple units. The woman that asked for this only wanted one, but as soon as I started working through the layout, I realized I could get four boxes out of a single 4' x 8' sheet of plywood. (Almost. I had some plywood laying around that I used to make two of the tops. Everything else came out of one sheet.)
The idea, though, is that if you're going to go through the trouble of making one, you might as well make a bunch, because it's only a little more effort. A lot of the work involves setting up jigs and templates, but once they're done you can just keep cranking them out.
I should also note that I have a pretty wide array of power tools. In most cases these just make things easier or faster, but many of them aren't a necessity. As I work through the instructions I'll try and point out how to adjust things if you don't have everything I do.