HDR stands for High Dynamic Range. It is a very general term and may be describing different techniques and applications.
The two most common uses in photography are:
1) Enhancing the tones in an image so that you can appear to display a greater range of tones (from dark to light) than would be possible on the output media using the correct tone mapping.
2) Merging 1 or more photograph at different exposures in order to overcome the limited dynamic range of digital cameras.
Of course, in some situations you could be doing a combination of the two.
I know little about 1) in situations were it involves mapping a single image.
Regarding number 2, consider this. You have a landscape scene with a wonderful sky with fluffy clouds and a forground partly in shade.
If you expose for the sky, the clouds will look wonderful, but you will have not have any detal (just black areas) in the shade. Conversly, if you expose for the shady areas, your sky will be blown out.
So you take two pictures, one exposed for the sky and one exposed for the shade. Usually you try to arrange this such that you only change the shutter speed and keep the lens aperture the same, you could also vary ISO on your camera as noise difference is minimal between 100 and 400 ISO.
Ideally a tripod should be used, but this is not essential with modern software as it can do a pretty good job of aligning images as long as they are very similar. This is way bracketing can be useful, you don't need to change anything between shots, just hold the camera steady, but you can always practise changing exposure without taking your eye of the viewfinder, or use reference marks in the image (what is in the centre ) so you are sure that the images are fairly well aligned.
Shooting RAW is better, but AFAIK, CS3 does not support merging RAW images.
The you merge the two photos together. This used to be very tricky, and it may be that some of the complex descriptions you have run into regard people who are still using older techniques.
I use PSP X2, CS3 has very similar features, but more of that later. Using HDR photo merge on the file menu you load the images you want to use. You can use as many as you like but I would start by using 2 or 3, inexperienced use of two many images will make things worse. Click the 16 bit option to get a 16 bit image out.
Once the images are loaded you can hit the align button, essential if they were not tripod shots. There are settings for brightness and clarify, I would suggest that you use the suggest settings button, this will get you in the ball park and you can fine tune later.
Once you have your merged 16 bit image you will find it appears to have quite low contrast, some PP work is generally essential to emphasize the photo the way you want it. If you have used RAW then you should probably adjust the WB first, if necessary. To get the right contrast, if you find curves tricky, then I suggest you use levels first, then highlights/midtones/shadows and possibly clarify, followed by normal brightness contrast to get the final image.
CS3 does pretty much the same, except that it does not do RAW merges, the alignment does not appear to be so good, it first makes a 32 bit image which then has to be downgraded to 16 bit to actually process, and many people say that the prgram often crashes (Personaly this has only happened to me a couple of times, and allthougth I have not used it much, my experience suggests that it is useable).
By the way, there is no reason why you can't use both, PSP is quite cheap and having merged the photos you can save it in PS format and transfer, that way you get the best of both worlds (I am assuming you prefer CS3 for post processing, you could just do everything in PSP which is what I do).
That should get you started. Start with an easy task, like the landscape with an exposure for ground and sky, then progress.