Find the wall studs beneath the stucco. A stud finder may not work in this situation, but you can bang lightly with your fist on the stucco wall and listen for a “solid” sound. Once you hear the sound, measure 16 inches down the wall and test for another solid sound. If you can’t find a stud every 16 inches, check every 24 inches.
Snap chalk lines, from floor to ceiling, on the stucco wall over every wall stud.
Install 1-by-3 treated furring strips in a single horizontal base row, 1 inch above the floor. The furring strips should lie flat against the stucco wall. Use concrete screws and a hammer drill to attach the base strip, inserting one concrete screw over each chalk line.
Install vertical furring strips along the chalk lines but leave a 1-inch gap between the base strip and the bottom of the vertical strips. This gap allows you to run electrical wires to outlets before hanging the drywall.
Position the first drywall panel, horizontally, at the top of the wall in one corner. The ends of the panel must meet in the center of a furring strip. This is called “breaking on center” and is essential for a smooth and secure wall.
Insert drywall screws every 6 inches along the edges of the panel and every 8 inches into the furring strips that run behind the center of the panel.
Position the remainder of the panels along the top row, butting each panel snugly against the previous one. When you come to the end of the row, you may have to cut the final panel to fit.
Install the bottom row of drywall panels next. Lift the bottom panels until they’re tight against the top panels before attaching them to the furring strips. This leaves a small gap at the bottom of the wall that you will cover with baseboard.