Before you decide what to bring on your trip to Alaska for Aurora viewing consider what time of year you will be visiting. The chart on this page is meant to give you a good idea of what the average weather is like. Pay attention to the average lows as they tend to occur at night, this is the time you will be out viewing Aurora. Soon before you depart for your trip you should check the long term weather forecast for a better prediction of what the weather will be like when you are here.
Base Layer: Feet
Having a base layer of insulation all across your body will greatly aid in keeping you warm and comfortable while out viewing Aurora. I would highly recommend wearing wool or a wool substitute sock.
Base Layer: Legs
Moving to your legs, there are two strategies that I find useful, either wear insulated or flannel lined pants or long underwear under the pants you already own. I personally prefer the insulated pants option because I dislike the feeling of long underwear and feel like it doesn't let my legs breath but if I lived in a climate where those pants would have little value I would just get long underwear to save money.
Base Layer: Body
I find wearing a long sleeve moister wicking shirt is the warmed base layer for the chest. Most of us have heard of Under Armour and their shirts work great but something like this Hanes shirt works just as well and will save you money. It is important that this layer is not cotton.
Next you should have a warm shirt like a flannel shirt or a wool shirt. Now that you have a nice base layer and a warm shirt you should wear a nice warm middle layer like a fleece jacket or this is what I personally wear.
Base Layer: Hands
Don't forget to bring some light gloves with you at a minimum. Some people like to wear light enough gloves that they can still operate their camera or use a smartphone app to control the camera. Regardless, this is one of the most difficult areas to dress for because of freezing fingers in cold temperatures and the need to use the camera.
Base Layer: Head
For temperatures closer to freezing you can get away with only one layer for your head. Something like this trapper hat will keep your head warm and help keep your neck and ears warm too. For even colder temperatures get something like this turtle fur that will add insulation to your head and provide a protective layer all around your neck.