Magnets taped to a drill and then spun in front of the screen is what someone mentioned.
Brushing away the colors with a normal magnet also works (deosn't degauss it, just magnetizes it to an appropriate field-whatever)
Best version- if you're ever throwing away a monitor or TV, just rip out the degaussing coil and use it. It's the thick wire running around the perimeter of the screen. They almost always rin on wall voltage- just splice the ends to a lamp chord.
Include a switch, or hold the plug in your hand so you can unplug it easily. It will vibrate a little and get warm fast, probably light on fire if left plugged in. Since you can get it right next to any point on the screen, it will be more powerful than any built in degaussing coil, and fix TV's with weak ones.
Also, since it won't fade off like a built in one, you've got to move it away from the screen when your done so it won't leave it's print.
I use one of these and it works great.
Just thought I'd post about it in case someone searches "homemade degaussing wand"