One practitioner of HDR photography is Sean McHugh, who has an online gallery of photos from his time pursuing a Ph.D. at Cambridge University in England. The image here shows Cambridge's King's College at sunset. McHugh's camera of choice is the Canon EOS 50D digital SLR.
In a nutshell, the HDR technique involves taking not one but several pictures of a given scene, overexposing some and underexposing others. The next step is to use specialized software, such as Photoshop CS2, to take all that data and construct a new image with a wider dynamic range.
Photographer Mathew Spolin explains how he took this HDR photo of San Francisco (posted on the Wikimedia Commons): "Another HDR - made from three exposures. To get these I hung the camera out of the eighth floor of the Mark Hopkins and braced it against the exterior of the building. The windows in the rooms open just enough to get the camera outside. I held onto the camera strap with my teeth just in case it slipped. Like many HDRs this one looks a lot better at the larger sizes."
This HDR image of Old Saint Paul's church in New Zealand, taken by photographer Dean S. Pemberton (and also posted to the Wikimedia Commons), was constructed from...
...six exposures using a Canon 350D. Exposure times from top left are 1/40th of a second, 1/10th of a second, half a second, 1 second, 6 seconds and 25 seconds.