I also really wanted to title this post 'How to Fix a Hole in a Sweater with Thread, Matchsticks, and a Q-Tip' so I'd sound more like MacGuyver, but I restrained myself.
Anyway. Take your sweater and find the hole. Turn the sweater inside out.
Grab matching thread. Or almost-matching.
Thread zee needle.
Okey-dokey. Start threading your way across the hole, beginning at the bottom. You only want to push the needle through the topmost bits of material, you don't want to push all the way through. If you do, you'll see the thread the next time you wear your sweater.
Turn zee needle around and go back the other way. Again, just catch a few of the topmost bits of fabric.
As you weave back and forth, very gently begin to tighten the thread. Don't tighten too much too fast, or you'll end up with a knobby bump in the fabric.
When you've gone all the way across the hole, turn the needle around and go back the other direction. Weave it, baby.
When you're done, it will look like a little woven patch. Tie your thread off, and you're done! Turn the sweater right-side out again, and ta-da!
The hole is gone.
Get ye gone, and save thine garments!