This is one of the easiest things to make. All you need is a blender and the ingredients. But don't cut corners on the olive oil. A cheap, bland olive oil will cheat you out of the joys of a fresh pesto sauce.
You can use walnuts, but I prefer using pine nuts to make pesto.
Well sealed in the refrigerator, a batch of pesto will keep for several days. Toss it with linguine, or serve it over a grilled or pan-fried chicken breast.
Now, here's a good recipe for pesto (although pesto recipes don't seem to vary much). This pesto recipe from Epicurious.com includes this interesting detail:
When combining pesto with pasta, Ligurians mix a small ladle of the cooking water into the pesto just before adding the noodles; this dilutes the concentrated sauce and helps it adhere to the pasta.
Interesting. I've never tried that.