In my former life I worked in a cabinet shop, and was exposed to all sorts of fanciful, specialized tools that most homeowners simply can't justify the expense for, like a $20,000 sliding carriage table saw. Or, even more modestly, a couple of hundred dollar pocket hole machine.
Having used and liked the pocket hole machine, I decided to build my own, using a router I found for a song at a yard sale, and with scrap plywood I got at the cabinet shop. The one I made was many moons old, and looks much worse for the wear, so it is modeled and rendered in 3D for your viewing pleasure.
Step 1: Commercial versions and basic use
There are some machines that are full size floor model machines, but the one that I based this design on was a Porter Cable bench tool that I used in the cabinet shop I worked in.
It is basically a router set up with a handle and a pivot. The picture is the only one I could find, and is of bad quality after zooming in and taking a screen shot.
The basic use of one consists of putting a board (usually) horizontally and the router bit either swings from the top or the bottom and creates an arced pocket so that you can basically toenail a screw into a board and it lets you butt joint two boards together.
Also shown is a picture of what the joint itself looks like- chances are that you have seen this on furniture even if you didn't know what it was.
There are also jigs you clamp on and use a drill with, the most notable being by Kreg. You can make those homemade as well, but I wanted a machine based version with a more dedicated setup. All other options were more expensive than I wanted to invest, so I made my own similar to the bench top model I was familiar with.