I have replaced the screen material in storm window screens. A neoprene cord wedges it into a groove in the screen. A tool that looks like a double barrel piza cutter stuff the screen in a groove, then the other end stuffs the cord into the groove to hold it.
Once I framed large windows into a patio under a deck, with pressure treated lumber. Stapled large sheets of screen over the openings, then finished it off by covering the stapled area with lattice strips to give it a picture frame look.
It might have looked better and gone faster if I had cut a shallow groove around the perimeter of the opening with a skilsaw, and used the neoprene cord to hold it.
Cheapest thing I can think of would be a roll of nylon screen and a frame made of lattice strips and staples.