The thing with pegboard is you have to put furring strips behind it so that it sticks out from the wall a bit, leaving space for you to put little pegboard hanging gadgets into the peg holes.
The window wall was pretty easy. We (as in, Shera) hung the furring strips on both sides of the window.
Guess what? You need a stud finder and a level and DRYWALL screws! Who'd a thunk it?
(Not me. Just another reason why Shera is so awesome!)
The other wall was a little weird because the people who built this house got very—uhm—creative. Finding studs was sort of a joke here. In another room, they'd hot glued very thin furring strips to the cement wall, then hot glued the wallboard to the furring strips.
On this wall, it seemed like maybe they'd used plywood behind the wall. But whatever they did, Shera was able to make it work.
Shera getting ready to attach the pegboard to the furring strips.
And ta-da! Here is the window wall:
And the other wall:
If you want to do this, just google "how to hang pegboard" and you can find a zillion instructions.
Next up: hanging vertical storage on the pegboards and moving in the furniture.