HDR photography is typically used with landscapes and inanimate objects, since it's hard to get identical shots with a moving subject when you're taking five to ten photos with different exposure settings. If you did try it in this fashion, you'd probably end up having major differences in the pictures that would destroy your ability to add the HDR effect in editing. Tripods are a necessity for taking the initial series of photographs. If you don't tripod it up, you're going to end up with the same problems you'd face if you were attempting animate objects in your photography.
Most SLR's have a multiple exposure setting which let you take 3, 5, 7, or 9 exposures. You'll want to set the difference between each photo to 1. This way with a 5 exposure shot you'll have 5 different photos ranging in exposure from -2, -1, 0, +1, +2. Simple right? It is.
Check the histogram on the camera to make sure that you're balanced throughout the photo before you begin taking it. Finally, a remote shutter release is a good, although not necessary, piece of equipment to use for this situation.
Once you've taken the photos, it's time to take the raw pictures to your photo editing software. I use the best HDR software on the market called Photomatix. Most standard photo editing software has HDR specific features, or a combination of features you can use to merge your photos into one HDR picture. It will probably take you some time to get used to this effect, and it does get very mixed reviews among viewers. It's a commonly used technique, and in some cases it's done very well and adds to the photograph, and in other cases it comes off as a gimmick. I tend to think that the gimmicky photos have amped up the painterly quality of the HDR processing. I tend to enjoy HDR photos which look close to reality, or the way I saw it when I was there.
If you aren't really comfortable with the photo editing software idea, some cameras do have HDR processing available directly on the camera. Instead of having to take it to an editing software, the magic happens right on the camera through its own features. This is handy if you want to get an idea of what you can do with HDR.
If you want a really advanced tutorial on HDR you have to check out Trey Ratcliff's classes which are an amazing series of videos. Grab them here. He leaves NO stone unturned.