I am a total sucker for HDR - Here's some of my attempts.
Since I started taking pics this has been the technique that most of my mates have asked me about. There are several tutorials on line about how to do this and most of them probably make more sense than this post but this is my take on it and hopefully you'll understand my ramblings.
So why do HDR? Well it's all to do with "Stops of Light" Here's a great tutorial on light stops and what they mean. So you see from that tutorial that a stop of light is just an arbitary phrase that indicates the amount of light you are allowing the camera's sensor to see. Increase your aperture by one stop doubles the light available to the sensor and decreasing the aperture by one stop halves the light available. You can also alter this using shutter speeds and ISO settings - but that's a topic for another day.
Anyway the human eye can make out good detail over about 20 stops of light - that's why on a bright day you can see the detail in the grass and the trees but still see the detail in the sky and the clouds. A camera sensor is a bit rubbish in comparison to the eye - your average point-and-shoot sees about 7 - 8 stops of light and a high end DSLR sensor sees about 10 - 12 stops of light.
If you go outside just now and take a quick snap of anything on auto mode and include about 30% sky you'll see that the sky goes completely white (or at least loses a fair amount of detail). You can compensate for this by using your camera's "exposure lock" function which should be in your manual - although the foreground may go dark. Also you can use a ND Graduated filter to darken the sky slightly which works really well. Here's some of Graham Stirling's work using Lee ND Grad filters (ND stands for neutral density incidently which means they block out some of the light without changing the colour).
There is normally about 2 stops of light difference between the sky and the ground and this might be even more e.g. on a bright day when you are standing in the shade. Your camera will try it's best to capture the middle ground and therefore dark bits might become silhouettes (also known as shadow clipping) and the lighter bits may become over bright (also known as blown highlights). These situatations can be a disaster and mean that you miss out some valuable parts of the whole shot. You can rescue some foreground detail and highlights but not if they are too black or over blown respectively - at least not without the end result looking weird.
So it appears that I've gone off-topic there but there was a reason - HDR!
As the name suggests High Dynamic Range is a technique that allows you to cover a high range of exposures or stops of light. This can increase that 10 - 12 stops I mentioned earlier to perhaps 16 or so. The concept is quite simple - you take several shots (usually 3) of the same scene - these are sometimes known as "bracketed" shots. Each shot takes a slightly different exposure - I normally take a +2 exposure shot which is over-exposed, a normal (or +0) shot, and a -2 exposure shot which is under-exposed.
This is the +2 shot. You can see that a lot of detail has been blown out in the sky. However, there is a lot more detail available in the darker parts like the water, the hull of the boat and the trees.
This is the normal shot or +0. This is the kind of shot that a point-and-shoot camera would take and what my DSLR took without and filters or exposure lock. You can see it's tried to make the best of the situation and keep come some of the highlights and provide some detail in the dark parts. This basically makes the best work with the mid-exposure range.
This is the -2 shot which is under exposed. The darker pasts of the picture as now almost black and clipped in some ares. This picture would normally be unusable but you can see that there is excellent detail in the sky and the brighter parts of the land.
This is where HDR comes in. You can use several programs e.g. Photomatix to then put all three pictures together. It'll take the useable parts from the three shots and create a final picture which looks like this...
Ok, so the purists out there will say that this is cheating and not a "real" photograph. To some extent I agree. It's a cheap way to give a mediocre shot a WOW factor that it wouldn't have otherwise. I certainly failed to work on composition etc when I started doing HDR. It's worth getting good at the basics first before taking this technique because it'll make an OK shot good but never great. All the other elements of photography have to be in use first to create that ultimate HDR shot.
Hope that helps you lot understand how to do this. Comments and critisisms welcome as always.