It's so easy! This brief video demonstrates how to extract DNA from your saliva:
Easily See Your DNA At Home - video powered by Metacafe
Yes, it really is the mucousy stuff you see at the end. If you're careful, you should be able to pick it up or spindle it around the end of a toothpick.
If you don't feel like running to the hardware store, rubbing alcohol used for cleaning cuts should also work for this experiment. Note, environmentally friendly dish detergents won't; you need the nasty sulfates.