Remove all debris, nails and screws from the basement walls. Use a paintbrush to help you get into the spaces inside of the ridges and channels.
Apply waterproof sealant to the basement walls. Depending on the sealant you choose, you may either apply it with a paintbrush or a sprayer. Allow the sealant to thoroughly dry before continuing.
Lean rigid foam board insulation against the walls of the basement with the flat side of the insulation against the wall. The side with the visible lip should be facing the center of the room. Place the boards snugly against one another so a channel forms when you place the two lips together.
Cut narrow furring strips to fit the basement wall. Place a furring strip into each channel between the rigid foam board insulation.
Drill screws into the furring strip, through the rigid foam board insulation lip and into the basement wall. In most cases, you will need 3-inch masonry screws to do this; however, if your climate requires a higher-rated insulation, you may need longer screws. Stagger the screws down the length of the furring strip to prevent the strip from splintering.