I've been drying herbs for years by just hanging them in my house or on the deck. But this year I broke down and purchased a dehydrator for drying other garden goodies, so I figured I'd give it a try for herbs, too.
This is a Nesco Gardenmaster dehydrator and I'm pretty fond of it. I scored it off of Craig's list for a darn good price. So far I've dried a TON of parsley (okay, maybe not a ton. But after drying and stuffing into a jar, it was a quart!), lemon verbena, sage, epazote, oregano, and basil. Next up are mint, apple mint, rosemary and lemon balm. 
The herbs certainly dry quickly in this thing- but not always in the 1-3 hours listed in the booklet. My basil took overnight to dry. Clearly less time than air-drying it, but I found myself getting impatient just the same. And it's kinda loud. When this thing is running I have a hard time hearing much else from the TV besides the loud techno music on my beloved CSI. I like to store my herbs in glass canning jars because, you know, I have millions of them. But resealable baggies work well, too. The key is to keep air in and moisture out.
The interesting thing about drying as preservation is that it doesn't actually kill any bacteria, mold, or anything. The preservation is possible because all these nasty bugs require moisture to live. By taking away the moisture, the bacteria (etc.) can't multiply. So if you're interested in killing any insect eggs (gross thought, but they're there, folks), you can either put them in the oven at 160 F for 30 minutes or in the freezer at 0 F for 2 days. I prefer the freezer method because my oven doesn't go that low and I hate to cook the herbs I so carefully dried- And both these methods are preferable to the irradiation that most non-organic herbs undergo!
