The Usual Solution: So the best thing to do is to limit the exposure of the cut surface to air, light, and heat. Many people simply press a piece of plastic wrap over the cut surface and stick it in the refrigerator. I've tried this and I've found it lacking. First, I don't like plastic wrap and second, it seldom creates a tight enough seal to keep the air out.
Another solution is to squirt it with lemon or lime juice but I've found that over time this just makes for a slimy avocado. Ugh.
My Solution: Place the avocado in a clean cottage cheese or similarly sized opaque container with a piece of cut up onion. Cover with lid and refrigerate. I've had a cut avocado stay fresh for several days this way. I don't know why this is, but I suspect that it has to do with the sulfuric acids that the onion releases. This is the same sulfur that makes you cry when you chop onions, but it is also used as a preservative. The onion smell/taste doesn't seem to transfer to the avocado, as far as I can tell. But I'm not overly sensitive to onions, so you may want to check this out first if you are.
The Guacamole Solution: Pressing plastic wrap over the guacamole to seal out the air and placing it in the refrigerator works really well. But if you want to avoid using plastic wrap, I've found that scattering some of the chopped onion called for in the recipe over the top of the guacamole, then wrapping the bowl in foil, or covering it with a plate, works really well. Just stir in the onion and serve!
Related: Recipe: Avocado Hollandaise
(Image: Craig Stephens)