The key to sucessfully photographing aurorae is to use the widest angle (shortest focal length) fastest (smallest f number) lens that you have in your collection, and the highest ISO that your camera can manage without excessive noise.  You'll also need a sturdy, stable tripod and some sort of cable or remote release for the camaera's shutter. 

Aurorae usually occur over a wide area of the northern (or southern for those in the southern hemisphere) sky, and are relatively dim although to the eye they can appear fairly bright.  A moonless night is best and if you're unlucky enough to have a full moon on the night that you receive a red alert, then expect any aurorae to be washed out.

Exposure times can be largely trial and error.  The intensity of a display will vary, as will the detail in a display.  I've suggested some rough exposure times below.  You can use these as a starting point and check the image afterwards.  If it's too dim, you need to expose for longer, too bright, expose for less time.  A good rule to remember is that the shorter the exposure time, the greater the detail you'll capture.  Aurorae can be fairly fast changing with areas appearing and disappearing in a few seconds.

You can clearly see the effect that lower ISO speeds and higher apertures have on exposure time.  Always remember that shorter exposure time means more detail.

Remember that cold weather can affect battery life so carry spares in an inside pocket. 

Don't forget to make sure your camera has an empty memory card in it and carry a spare or two.

Last but not least, take some time for yourself and enjoy the spectacle!