Serve it on pasta, with eggs, with cheese, on crackers, with chicken or fish, worked into pasta or tortillas or with just about anything else that needs fantastic flavor. I recently ate some marinated artichoke hearts that had been tossed in pesto - they were excellent.
Step 1: Basil and garlic
Pulse several cloves of garlic in the food processer, then add handfuls of basil until everything is chopped. The bowl will be a nice emerald green color.
Step 2: Toast Pine Nuts
Step 3: Add other ingredients
Add pine nuts, extra virgin olive oil, parmesan cheese, and salt to taste.
The olive oil controls the consistency- add more for a softer blend. More parmesan makes it more crumbly.
If you plan to freeze your pesto, don't add the cheese! It doesn't take freeze/thaws well, and is easy to add after you've defrosted. You can add lemon juice to prevent oxidation.
Freakish (but tasty) variations:
If the basil turns out to be slightly bitter, you can add some honey or agave nectar. Salt, pepper, chili powder, and Worchestershire sauce are frequent additions. Taste to see what you like. If you're trying to make vegan pesto by skipping the cheese, add more salt and up the nuts and weird flavorings to make up for the taste, as Parmesan is pretty strong!
You can make all sorts of wacky versions- forget tradition, figure out what tastes good to you, and create something new. If you come up with a particularly good pesto derivative, put it up as a new Instructable for everyone else to try!