Cut and Hang the Drywall
Use a tape measure and a pencil to transfer the dimensions of your box frame onto the sheets of drywall. Then, cut the drywall with a utility knife (Image 1). The strength of the drywall is in the paper, so if you simply cut deep enough to get past the paper on both sides of the sheet, the sheet should separate easily by bending.
With the drywall cut, install it to the framework using drywall screws (Image 2). The marks you made on the wall and ceiling in Step 5 will help you find the studs when screwing the drywall to the frame.