A HDR photography overview
High Dynamic Range (HDR) photography is the process of capturing multiple different exposures of the same scene, which are later combined, or blended together in post-production, with the aim of producing an image that has good or perfect exposure throughout.
Imagine a simple landscape scene - some lovely green hills, backed by a nice blue sky with some puffy clouds. In a scene like this, there will be a big contrast in brightness between the foreground (the hills) and the background (the bright sky), and this massive difference in brightness will make it very difficult, if not impossible, to photograph this scene and have it turn out the way that it appeared first-hand (through your eyes). I'm sure you've experienced it before - your photo ends up with hills that look ok but a sky that is way to bright/pure white, or a sky that looks nice and blue but hills that are completely black! The HDR technique is one of the most effective post-production methods to overcome this issue.
Sounds good, how do I do it?
Besides of course your camera, it is vital that you have a tripod for HDR (regardless of the time of day/amount of light). Also, it is greatly beneficial to have a cable remote for the camera - allowing you to adjust settings without actually touching (and possibly moving) the camera.
Once you have identified a scene where HDR may be beneficial (high contrast scenes are a good starting point), get the tripod setup, switch the camera into manual control mode (sorry, you must have a manual mode!) and compose/frame the shot. You should ensure that both ISO and White Balance are locked at custom values, rather than set to Auto - we don't want them to change from shot-to-shot! Now set your desired aperture and shutter speed which give a good overall/average exposure for the entire scene.
The object is to photograph this exact same scene (yes, this means that the camera cannot move, at-all!) multiple times by bracketing the shutter speed above and below the initial average exposure. Notice that I said 'bracketing the shutter speed', which means that the aperture value should also remain the same between shots - we do not want the depth of field to change. So, all that should change is the shutter speed. So with that in mind, you can now go ahead and photograph the scene, varying the shutter speed each time (ideally using a cable remote, rather than touching the camera).
As an example, if I have composed a shot and determined that the average good exposure for the entire scene is 1/160th second, I would go ahead and shoot one shot at 1/160th, and then maybe one at 1/320th (minus 1 stop/darker), and one at 1/80th (plus 1 stop/brighter). Or, depending on the scene and the amount of contrast variation, I may even decide to shoot two shots below the average and two shots above the average - so I would shoot as above, but in addition I would also shoot one shot at 1/640th (minus 2 stops/much darker), and one shot at 1/40th (plus 2 stops/much brighter), giving me 5 shots in total. Of course, the number of shots and the amount by which you vary the shutter speed is all flexible, and different combinations will give more pleasing results depending on the scene - it certainly takes come practice.
So after going out and photographing for HDR, you'll be left with a bunch of photos that, to be honest, probably don't look very good as they are. They now need to be combined, for which you will need your computer, some software and a little patience. Unfortunately I am not going go into details about how to perform the edit, but I will get you started. A fairly popular option, and probably the easiest/least technical approach is a program called Photomatix, by HDRsoft.
HDRsoft offer a free Photomatix demo version on their website, and for those of you who are less computer savvy, or cannot commit much time, I completely recommend it as it automates much of the process and takes out a lot of manual effort. But of course, being heavily automated does come with down-sides, and I have found that often I just cannot get the result that I was aiming for with Photomatix. That's why I personally prefer to do the edit manually in Photoshop, by simply importing each exposure into a different layer of the project, and erasing from each layer the parts which I do not want in the final image, using a very soft-edged brush. It takes some time, but I think when done well the results speak for themselves.