When we stay at state parks, we usually bring the electric chain saw (so we don't bother the entire campground), a splitting maul and splitting ax. We ask the Rangers if it is okay to cut dead trees that are still standing to use for firewood. We've never been told no. Then we'll spend a few hours cutting and splitting and usually have more wood than we need.
When we stay at private parks, we usually just buy it from the campground. Usually it is reasonable, if it is not, we'll look around the immediate area. Usually someone is selling bundles of firewood close to the campground.
-Michael