The basics of getting good aurora photos:
A digital SLR (aka DSLR), while not necessary, is the best place to start. At the very least, you need a camera that will allow you to manually set the shutter speed (exposure length), aperture (f/stop), ISO, and focus. It should ideally be mounted on a tripod, with at least one spare memory card and fully charged battery on hand. It's easy to fill a memory card in one setting, and if you live in a colder climate, (northern latitudes increase your chance of seeing aurora) batteries don't usually last very long in frigid temperatures. A tripod is critical, as it is impossible to hold a camera perfectly still for the length of time it takes to expose these shots. In a pinch a beanbag and timer setting on your camera will do.
Your aperture must be open as wide as you can get it. Narrow apertures can seriously limit the quality of your shots.The shutter speed will need to be between 2-30 seconds depending on the intensity of the light. If you're st