To photograph at night you will need a tripod to minimize camera shaking. Handheld aurora photos will not be sharp. To adjust settings comfortably, the tripod should be nearly your height.
Your camera needs to have the option of manual focus and a complete manual mode which allows you to adjust aperture, exposure time and ISO separately. Best cameras are dSLRs (although new mirrorless cameras are good as well). here you can put on a good lens for the night and will get the best quality.
You should use a fast lens (meaning wide aperture, with a small f-number like f/2.8 or better) to make the most of the available light. Lenses with f/4.0 are doing fine also but you will have to crank up the ISO. Auroras often stretch all over the horizon. To capture a big part of it, you want to have a wide-angle lens (24mm or wider).
To further minimize camera shaking, use a remote control for taking pictures without touching the camera. Many cameras have a delayed shutter mode (1sec..20sec) which is a good alternative.
In cold weather your batteries will discharge quite fast, so it is important to have at least one extra battery with you. Using hand warmers, you can revive the batteries to get the last bit of energy out of them (tip from Jake D., thanks buddy).
At times you will be in damp weather or it will be windy. Moisture can be a problem especially in low temperatures. Your lens will get icy. One way to delay that problem is putting the sun hood onto the lens.