A pretty simple project, probably 30 minutes if you have the tools handy.
The parts list for this one is pretty short:
*The smaller the circuitry inside, the better. I managed to find a 16GB at microcenter that had 100% of the circuitry inside the usb plug itself. The rest of the internals were just a plastic dummy board. This type is ideal, but I'm sure normal flashdrives will work if the LED is sanded flat to fit, or if you use an SMD LED.
Once you have the innards out, probe around with your multimeter to find the 0v and 5v pads/traces. The easiest place to solder the LED to will likely be where the plug connects to the circuit board. In my case I had no such circuit board, so I soldered to where the contacts terminated into the memory chip. For reference, in this view the large top contact is 0v and the bottom large contact is 5v.
I went the deadbug route with my soldering. I cut off most of the LED's negative lead and replaced it with my resistor, then trimmed the leads down to length and bent them so they matched up with my power pads. A couple quick touches of solder and we're in buisiness