The green bed sheet provides a color that isn't normally in the scene (ie -- the costume isn't green, skin tone isn't green, props aren't green, and lighting isn't green). Then, using a program that can remove the green color channel (remember, video and computers use the RGB (Red, Green, Blue) color space), and can also layer the video (like layer pictures in PhotoShop, you can easily create the appearance of being in front of a different background, or a whole other room. Its the same concept that puts a weather map behind your local weatherman on TV. We use Final Cut Pro on the Mac, but any high end video editor like Adobe Premier and Sony Vegas (do they still make that?) can all do it to some degree. Your best bet is to use a high end digital painting (Adobe After Effects) or compositing program (Apple Shake).

Oh yeah, I should also point out that the exterior shots we taped outside at a park, with a hill in the background (intended to block the local neighborhood from view), and the sky was over exposed to remove any cloud features. We then used the same concept as the green bed sheet to remove the sky color (which was white), but instead selected the sky's color to "key out" using a color tool. We then layered a still picture of the temple underneath the park video, and layered the foreground pillars on top of the video. But you have to plan shots like this using storyboards and blocking for your actors.