my day job is as a video producer, so I can help you out. Lots of inexpensive video cameras take very nice video nowadays. A friend of mine just got a hundred dollar panasonic lumix digital still camera that takes pretty darn good 720p hi-def video. Definitely not professional quality (it lacks pretty much any manual adjustability - a must for professionals), but for something like ed's video above, it'll work just fine.
Your two biggest issues are going to be lighting and audio. Ed's video has very good basic lighting. There's a large
softbox or something similar to the right of the camera with probably a 300 or 500 watt light, as well as a fill light low and to the left to minimize shadows. You can probably make do with a worklight from a hardware store and some foamcore. Aim the light away from you directly at the foamcore, and it will bounce soft, even light back at you. This should cost less than 100 bucks, rather than hundreds (or thousands) for a video light setup. Look up an article online about 3 point lighting to get the basics, and you should be good to go.
As far as audio goes, You'll need some kind of direct or close-mic recording for the bass, plus a mic to pick up any speaking you plan to do. No on-camera mic will get the whole job done with any kind of quality, no matter how great the camera is. So we're probably talking some kind of mulit-track recording into a computer, and at least 2 inputs. I suppose you could record your dialogue with the on-camera mic, and then record your bass directly into your computer, but the sound might be iffy for your instruction.
Once you've got everything recorded, you get to sync the audio and video you've recorded and edit your piece together! For syncing, I would suggest hitting record on the camera and your computer, then smacking your strings over your pickups lightly. That'll make a very fast transient audio cue that will be relatively easy to sync with the video. Then DON'T STOP RECORDING until you're done or out of tape. If you stop recording at any point, you'll have to sync things more than once, and that can get to be a big pain.
As far as editing software, iMovie on the Mac works well, and I think windows movie maker on the PC will get the job done for free. If you're willing to spend a bit of money, Final Cut Express on the Mac, and Sony Vegas on the PC are good choices for under $500.00.
So once everything is sync'd, cut out the bits you don't want so you have a decent finished product, then upload it to youtube!
I hope this is helpful! Feel free to ask more specific questions, although I don't know much about consumer-level cameras.