Answer:
Well, it depends on where you are in Alaska. The shortened days of sunlight are caused by changes in the angle at which the sun's rays hit the earth as the earth rotates around the sun.
I am in Juneau (latitude 58.37 north, longitude 134.58 west), down in the southeastern part of Alaska. Here, on the summer solstice (about June 21st), we get about 18 hours of daylight. Then, we start losing about 5-10 minutes of daylight per day until we get to the winter solstice (about December 21st). On the winter solstice, we get about 6 hours of daylight. Then, we start gaining 5-10 minutes of daylight per day until we get to the summer solstice and the cycle starts over again.
Farther north, the differences are even greater. In Barrow (latitude 71.30 north, longitude 156.78 west), at the northern tip of Alaska, it really is the "Land of the Midnight Sun". Near the summer solstice, from about May 10th to August 2nd, the sun never sets. And near the winter solstice, from about November 18th to January 23rd, the sun never rises. At other times of the year, Barrow gains or loses daylight just like Juneau does.
Those are the two extremes. The rest of Alaska is somewhere between those two. For example, Fairbanks, in the middle of the state, gets about 20 hours of daylight on the summer solstice and about 4 hours of daylight on the winter solstice.
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Another contributor contributed another way to look at it:
Anyplace on earth that's farther north than the Arctic Circle, or farther south than the
Antarctic Circle, has at least one day a year when the sun doesn't rise, and at least
one day a year when the sun doesn't set. The closer you get to the poles, the longer
these annual periods of no sunrise and no sunset get.
Most of Alaska is south of the Arctic Circle, and has a sunrise and sunset every day of
the year. The Arctic Circle crosses Alaska on the line roughly through Shishmaref, Allakaket,
and Fort Yukon. North of that line is where you can have 24 hours without a sunrise
or 24 hours without a sunset.