HDR stands for High Dynamic Range which pretty much tells you everything you need to know, right?! However, just for fun, let me try to explain what it is / why you should use it, and how to set up your camera for it!
Don't search for HDR photography. You will see absolutely horrible examples.
What is HDR and why should I use it? HDR is a technique used to reproduce a greater dynamic range of luminosity than is possible with standard photographs. How often do you see something you want to capture only to look at your photo and see areas under or over exposed? If you're always wondering why that happens, It's actually pretty simple. Our eyes see a much larger range of f-stops when compared to any camera. That's why when you are in a dimly lit room with a window you can see both inside and outside while your camera can only properly see one while the other is under or over exposed. HDR is how you can fix that.
An HDR image is typically made up of at least 3 photos taken at different shutter speeds resulting in a bright, medium, and dark photo. Think of the scenario above... By shooting 3 images at different shutter speeds, we would have one where the outside looks properly exposed, one where the whole scene is neutral, and one where the inside looks properly exposed. Taking these three images into a program such as Photomatix Pro or Photoshop's "Merge to HDR" allows you to combine them into a single image where everything starts looking like the way you saw it with your own eyes.
Just remember: with both Photomatix Pro and Photoshop's "Merge to HDR" you can overdue the effect and end up with photos that start looking like a cartoon. However, if that's the effect you want, go for it! Play around with the settings until you are happy with the result. There is no perfect solution.
How do I set up my camera for HDR? I always try to shoot my HDR shots at ISO 100 and in Aperture Priority mode. Aperture Priority can be set on any camera by turning the dial on top to the letter "A"/"Av" or by changing your shoot mode to "Aperture Priority" from the camera's menu. I'll explain why I use Aperture Priority in my next blog post. Next, you need to turn on bracketing mode to take multiple exposures. I currently shoot with a Sony, but I'll run though how to set up a Canon and Nikon as well. For any other cameras, just look for a similar setting since it's usually labeled the same way.
Setting up your Sony: Go into the MENU and find "Drive Mode." Change the drive mode to "BRK C 2.0EV3." That means you are taking 3 images; one 2 stops under exposed, one neutral, and one 2 stops over exposed. FYI - There are button shortcuts to get to "Drive Mode." If your camera shows anything other than "BRK C 2.0EV3" change it by going into the "OPTION" menu or by pressing right or left on the back dial.
Setting up your Canon: Go into the MENU, find "Expo.comp./AEB", and press the SET button. Spin the top dial until 3 or more lines spread out and align with -2, 0, and +2. Now press the SET button again to confirm your settings. You are now taking 3 images; one 2 stops under exposed, one neutral, and one 2 stops over exposed.
Setting up your Nikon: Press and hold the "BKT" button on the outside of your camera, and spin the back dial until you get to 3F (or more). The camera should automatically show 3 lines on the top screen aligned with -2, 0, and +2. That means you are taking 3 images; one 2 stops under exposed, one neutral, and one 2 stops over exposed.
If you don't have a remote, change your camera's settings so it has a 2+ second delay. This way you can set everything up on your tripod, press the shutter, and step back while it takes all 3 images.
Good luck and happy shooting!