For each button, select it and then enter the corresponding keyboard key in the field to the right (this shows when 'Press Key' is selected in the drop-down box)
It was a bit tricky, as I had to go into my emulator and change the keyboard configuration to match what I was doing in USB Overdrive. I gladly paid the $20 once I got it working correctly. The developer asks users to pay $20 for it, but you can download and run it for free if you're willing to wait 10 seconds each time you run it. This is a plugin for System Preferences that lets you detail what each button does, and ensure that it only applies to particular applications.
However, I'm sure it's pretty much identical to other brands of NES/SNES USB controllers out there. I found a solution! For the record (and for Google search results' sake), I'm using the GTron (G-Tron) USB SNES controller or gamepad.