You unlock the camp iirc about 2 hours in out of 40ish. Trying to put this with a minimum of spoilers, the current content ends after you finish Deepwoods Heart, report back, do some camp scenes, and get blonde and blue haired party members (not Sam).
On the bottom left there should be a few buttons, like Adventure, Allies, etc. Allies lets you talk to characters and pursue their various plotlines, Adventure takes you into adventures which are the main way to progress the plot. As you get further in, new buttons will appear (some temporary, some permanent) for one-off scenes or new areas.