Measure the height of your basement wall from floor to ceiling, using the tape measure, beginning in one corner of the basement. Transfer this measurement to a piece of drywall and cut it to that length with a utility knife.
Measure electrical outlets, windows or other features that fall within the area to be covered by the first piece of drywall. Transfer these measurements to the drywall and cut out a space to accommodate the features.
Stand the drywall up and press it against the wall. Secure the drywall to the studs behind it by driving drywall screws through the drywall and into the studs. Put in a screw every 12 inches vertically and spaced horizontally so that they meet the studs.
Continue to install sheets of drywall in the same manner around the perimeter of the basement, pressing each one closely against the previous one to create tight joints between them.