In the summer, you really have to reserve a campsite. Reservations must be made 2 days in advance. DNR campgrounds available:
Pinewoods campground (the northernmost)
Ottawa Lake campground (it's the southern of the two north campgrounds)
Whitewater Lake campground (south end)
TODO: Call and find out how they handle reservation no-shows. It looks like campsites are reserved WAYYY ahead of time, so there are probably a lot of "short-sat tables", from people snapping up sites even when they're unsure they will actually go.