You may make reservations online, through a third-party reservation system. Reservations are possible as early as December 1 of the year before you wish to visit (e.g., Dec 1, 2015 for a 2016 visit).
There is no easy answer to the question "Are reservations necessary?" Park campgrounds fill up sometimes, but not every night of the summer. If your schedule is very inflexible, and/or you know you want to camp in Denali (instead of one of the campgrounds outside of the park), then it is smart to make reservations in advance. If you wish to keep your Alaska travel plans loose and do not want to be bound by a reservation made months in advance, you can wait til you are here, or until shortly before you arrive, to try making reservations - but you might find limited availability.
Campground fees vary a little, but sites are all around $12 - $27 / night. Camping is free in winter (roughly late September - May 14 each year). Senior Pass and Access Pass holders receive 50% off nightly camping fees.
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