Green screen footage, or keying, is one of the most basic processes in visual special effects. It allows film makers to capture something on video, but then easily remove the background during post-production, and replace it with digital assets. Here's a quick tutorial on how to do this yourself.
Traditionally, removing unwanted elements from a video was done with rotoscoping, which is basically outlining the character you want to keep, and then manually get rid of everything else, frame by frame. It's still something that's done constantly, although modern software makes this process faster. But if you can shoot with a green screen, it removes the need for rotoscoping, and instead allows you to get rid of these elements in one fell swoop.
When preparing your shot, it's important to cover the things you want to remove with a uniform green screen. It doesn't have to be the background, it could be foreground elements as well. The most important part of this process is to have the green be as similar as possible everywhere, with no change in color. Lighting is especially important, because if shadows spill onto the green screen, you may have poor results. Also, since the point of the green is to have an easy to spot color, make sure none of your actors are wearing green.
Once you have your video, you can use one of many professional editing software to do the keying. Final Cut Pro, Adobe After Effects, they are all used by professionals to do this. If you're just starting out however, I recommend looking at PopVideo
which is a simple app that provides one-click keying.
Simply load your video, then click the button on the upper right. Then, use the first slider to control how much green is removed. After you're satisfied with the result, you can use the very last slider to add blur around your characters so they mesh in better with the assets that will be added. PopVideo costs $100 and comes with a demo, although that demo adds watermarks so you will need to buy it to actually use it.
Once you've got the video done, you can save it in a transparent format to use on the web, or to import in other programs such as 3D animation software.