Step 1: Parts needed
-62ish OHM resistor***
-LED of your choice
-Old USB plug
-Twisted wire or hookup cable
-Relatively stiff wire (doesn't have to conduct electricity)
-Some tape (electrical is probably the best)
***Resistor may vary depending on your LED needs. Source voltage is about 5 volts from USB. I suggest this website if you don't want to second guess yourself: http://led.linear1.org/1led.wiz. I use it all the time because I doubt my math abilities.
Step 2: Cutting
Pro Tip: Don't use a USB plug with shielding like I had. It makes it far more annoying to cut up with shielding.
After you hack up the USB plug, find the positive and negative wires. Don't assume that red is positive and black is negative. Never assume in electronics. In my case, yes red was + and black was - :). But I checked and that's what counts. Cut the other wires if any, you just need power.
Step 3: Soldering the LED
Step 4: Soldering the USB Plug
After it's all soldered up, plug it in and make sure it works. This is important in case something was messed up. You don't want to finish the project just to find out a wire was wrong or a solder joint was bad. After you confirm it's working, seal the joints with tape or some liquid tape. Cram the wires on the USB side back in to the sheath as much as you can and then tape it back up.
Step 5: Giving the wires support
Step 6: Make it pretty
Step 7: Other thoughts
-Use a potentiometer (like a 0-200 ohm pot in series with a 62ish ohm resistor) for variable light.
-An on off switch
-Use magnet wire so you don't have to have the conducting wire and support wire separate.
-Have the LED swappable so you can change colors.