I live in Kenai, In the darkest part of the winter the sun comes up about 10am or so and starts to go down about 4pm. In the lightest part of the summer the sun will go down below the horizon so you cant see it but not far enough that it gets dark, its like where you live in the morning where it gets light outside but you cant see the sun yet.
As far as dealing with it, never been a problem. And in the summer makes for more hours outside fishing, hanging out with friends, bar-b-ques etc...
Alaska has to to be the most misunderstood State in the nation. Yes we have almost 24 hrs of daylight in the summer just gets dusk like at night 2 to 3 AM. But winter 75 miles North of Anchorage starts at about 3PM and gets light at about 9AM. Not bad if you are out and about during daylight hrs. We have dog races starting in Jan and going till about 3rd week in March. There are also sno-gos, and ice fishing, cross country skiing, snow shoeing, for the outdoors set. You need to get out and experience the good winter weather. It is best after it goes below 0 and the water is froze out of the air. -40 is not bad if you bundle up for it it is a dry cold, better than down south where it is damp and chills you to the bone.
You only have constant darkness well north of the Arctic Circle. Even on the shortest day of the year, at the Arctic Circle, where the sun does not come up on that day, there is still a long twilight. The summers also have endless light up north. Of course, Alaska is so big, these generalizations about light and dark do not apply tot he whole state.
Fairbanks is about as far north as most people would actually move to in AK...and winters have at the minimum 2 hours of solid daylight at the very least. Not guaranteed to see the sun though...if it's clear enough to see the sun, it's VERY cold. High pressure systems in the winter bring clear skies and 30 below or colder. It's warmer when it's overcast. In the summer, it's as described...a month straight you can actually see the sun for 24 hours, and nights don't get truly dark until mid-september.