Step 1: Supplies
knitting needle #9
Note: In place of a knitting needle, you could use a...
plastic or metal rod or tube
...anything long enough to wind on that's rigid and will fit in the drill chuck. Here I used a size 9 needle. You could go larger or smaller as long as it seats properly in the chuck and spins without wobbling.
Step 2: Setup
Tape the yarn again, right at the base of the needle, close to the chuck.
The tape doesn't have to be any particular distance apart; just far enough for your yarn ball to form in between them.
Step 3: Begin Winding
As it builds, start moving your guide hand back and forth a bit faster so the yarn winds on a diagonal. This is loosely similar to what a commercial winder does, and helps it hold together when it's finished. The diagonal winding will be evident in the next step.
Step 4: Finish
Take the needle out of the drill, remove the tape and slide the ball off of the needle.
It is messier than a ball from a commercial winder, but just as functional. If the looks bother you, you can wrap the last few layers by hand to neaten up the outside.