Recently I've had the chance to repair a charger from a Nintindo DS Light that a dog had destroyed. Useing what i had handy, and spending nothing this is the end result.
First get your cables together. An average USB outlet has an output of 5V. The output of a Nintendo DS Light charger is 5.2V. In short .2V under is fine.
Step 2: Collect Tools
Some Things that you Need
-needle nose plyers
these are helpful
Step 3: STRIP!
strip your cables down. on the DS cable strip back the insulation to reveal a red wire and some copper wire. strip the red wires insulation back some. on the USB cable keep the red and black wires and trim everything else back. strip some of the insulation back from both.
Step 4: Connect Wires.
Useing Electrical tape, shrink tube, etc. connect your red wires. black goes to uninsulated copper. (helps to twist it together)
Step 5: Test
test your work. everything should have been easy.
Step 6: Clean It Up.
clean up your work if you care about looks. I just tightly wrapped it up with electrical tape then heated it with a lighter to shrink it tight. and that's it.