Backgrounds for the chroma-keying process are nearly always a specific shade of green or a specific shade of blue. The most important consideration for choosing the method you will use to create your background is the evenness of the blue or green color. If you think about it, this makes sense because during the postproduction process, you're only going to want to have a single tone to remove from the shot. The more tones there are--a black line where two green backgrounds meet, a darker wrinkle in the fabric--the more chance there is you will get an uneven key. Although you can expand the range of shades to "key out" of the shot, you run the risk of keying out parts of the subject as well, making an unusable final product.
There are a wide variety of methods to create the blue or green background. Painting a wall or a series of boards using special chroma-key paint available from film and video supply stores is a good way to create an even surface that is more permanent. If you paint a wall, avoid areas with wall outlets or bolt a curved heavy paper or a flexible board to the wall from just above the outlet and curve down, masking the area where the wall meets the floor and out a foot or two. You'll want to fill in any cracks with sealant and make sure to paint those, too. Some nice, in-depth articles on the construction of particular chroma key backgrounds exist on the Internet (see Resources). Fabrics exist as well, but you'll have to be sure they are both completely opaque and entirely free of wrinkles.
Once you have an even chroma-key background set up, you have to light it evenly. Don't be stingy on your use of lights, but don't go crazy with it. Light the whole surface well and then stop adding lights. Too much light will cause a green or blue reflection on your subject. Your subject should be far enough away from the backgroun--a few yards or meters--that they won't cast any shadows, either. Light your subject independently from your background. Make sure the subject is not wearing any shade that matches the chroma-key background. White has more of a tendency to reflect blue or green from the chroma-key background, so it may be best to avoid it, although a good lighting job should do the trick to avoid this, as mentioned above.
Once you have chroma-key footage, you have to edit it on the computer in order to remove the chroma-key tone and replace it with a separate background. Some common programs used to do this are Apple's Final Cut Suite, Adobe Premiere or AfterEffects and Sony Vegas. There are other programs specially made for chroma-keying effects, such as Serious Magic (now bundled with the Adobe Production Suite), Ultimatte and Mattinee. Before doing anything to replace the color, if your program has the ability to do so, apply a garbage matte or mask around your subject to exclude any areas of the footage that are unnecessary to retain, such as extra sections of wall. After the mask is applied, start excluding shades of either green or blue, depending on the shade of your chroma-key background.
After you are fairly satisfied that you have removed all of the back, you'll probably want to soften the edges of your subject and apply a spill suppressor, if your program has one. A spill supressor adds the opposite tone of your chroma-key to the edges of your subject, reducing either the green or blue reflection, or "spill" on the subject. After this is complete, it is time to add the new background as a layer underneath you subject.
Finally, color correct your subject layer to try to match the look of the background. When this complete, you'll have a realistic-looking chroma-key.