I did a bit of research, and tried 4 different systems this year.
Drying: I hung mine in an upside down paper bag, to dry in the garage for a few weeks, before stripping the leaves off of the stems and grinding it in mortar and pestle. You don't get a lot of basil bang for your buck this way, an entire bunch seemed to net a few tablespoons.
Oil preserving: This olive oil and basil paste is supposed to last a year, if you're careful about covering the top back up with a thin coat of oil after each use. Just give it stir when you need to use it, then cover with oil again when you're done. Seal it tight.
I haven't blogged about my mini foodsaver yet, but I love that thing. I vacuum-packed and froze quite a few bags of basil leaves.
And more freezing. Another means that provides you with fresh-like leaves in the winter is simply freezing basil in water. I cut mine into thin strips, crammed it into an ice cube tray, covered it with water and froze it.
Pop these out, toss 'em in a plastic bag or container, and you've got basil at your fingertips for the next sauce or fried rice you whip up.
