Zach Arias offers up this lighting tutorial on DEDPXL to show you how to light for a seamless white, black, grey (virtually any color, really) background. If you're a stickler for details like me, one thing you'll appreciate is the utter thoroughness of the lesson. Arias breaks down not only the hows, but the whys behind every creative and technical decision he makes on his set. Check out Part 1 below. (You can also find out more in his blog post here.)
Now, not everybody can afford the equipment or the space that Arias is able to utilize in his tutorial, but there are certainly some cheap workarounds that you can use to get the same effect. If you don't have the cash to spend on professional backdrops (Arias uses a Photo Basics 9×20 high key white fabric background), fabric stores carry all sorts of materials that cut down on creases and wrinkles and effectively distribute your light evenly. Muslin is usually the go-to, but velvet, fleece, and duvetyne work well, too.
The key to getting a nice seamless background is starting out with a background that can be made to look seamless in the first place (no wrinkles). After that, following Arias' advice about light/subject placement and camera settings will take you the rest of the way. Keeping your subject far enough away from the background (about 9') will allow you to light them both separately and avoid spilling unwanted light on each.
Background lights: excessively bright vs. just rightCredit: DEDPXLThough Part 2 of Arias' video series deals more with still photography, there are some tips on working with your materials in post, which you can adapt to whatever you're working with. You can check out the video below.