I'd written a nice, long reply to this post a couple days ago, but the web page errored-out. Here's a shorter version..
A green screen is just that - a piece of material with a special green color that is not normally found elsewhere. While editing, this color is keyed-out by your software, making the background - or anything that was close to this shade of green in your video, become transparent. This now allows you to place an image or other video in an underlying video track.
To take an example, I'll borrow Ralph Cramden's line (thus giving away my age) and send my wife, Jean "to the moon". Jean stands in front of a greenscreen and I shoot some video and subsequently capture to my computer. I key out the green background and drop an image of a closeup of the moon's surface in a lower video track. "Presto"! I have sent Jean to the Moon, something Ralph was never able to do with Alice.
NLEs like Premiere Pro have limited greenscreen key capabilities, but they're generally good enough for web videos, iPods, etc. For really good keys, you'll need something like Serious Magic's Ultra or Adobe's After Effects. You'll also want a really good 3CCD camera with at least 1/3" chips. Ultra 2.0 will let you shoot with the camera in a "portrait" position (using still photog terms), effectively increasing your resolution by 50%.
We do quite a bit of greenscreen. Before a shoot, Jean spreads the huge sheet (Purchased from Adorama, I think) on the floor and irons it carefully. This step takes over an hour - much longer if we haven't locked our two cats in the workout room!
Then we hang the backdrop on backdrop stands and let it extend forward on the floor so that subjects will be actually standing on the greenscreen (careful not to make wrinkles as they step).
Lighting a greenscreen is almost an art. You want the light to be very even, no shadows or differences at all. You must keep your subject(s) at least eight feet or more from the backdrop to avoid green light spilling onto them, creating an edge that won't look right. A back light will help provide separation and a reddish filter may help fight the green spillage.
Lighting your subject is different too because you must keep shadows from falling onto the backdrop. This often means that key and fill lights will be at greater angles.
To get started, especially for Web video and iPod, you don't really have to invest in an expensive greenscreen, etc. You can buy a green sheet at Walmart or dye one. It may not key as readily as a "real" one, but it'll be a lot cheaper!