Measure the length and width of the room. Multiply the length by the width of the first side and multiply the two together. Repeat the process for all of the other sides and add the sides together to determine how many sheets of sheetrock will be needed for the installation.
Place the first piece of lead-lined sheetrock in any corner of the room, with the lead pushing up against the studs on the wall. Attach a 1/4-inch drill bit to a power drill and drill pilot holes through the drywall and into the stud behind it. Space out the holes every 8 inches down each stud.
Insert a sheetrock screw into each of the pre-drilled holes down the entire sheet of sheetrock. Butt the second piece of sheetrock up to the first and install it exactly the same way. Continue around the entire room, installing the lead-lined sheetrock into the studs until the walls are complete.
Install self-adhesive sheetrock tape over all of the seams between the pieces of sheetrock. Run the tape over all of the seams and cut it off at the end with scissors. Mix a tub of joint compound and spread a layer over the sheetrock tape with a taping knife. Cover all of the seams in an upward motion with the knife. Let it dry overnight.
Sand down the area with medium-grade sandpaper until the surface is smooth. Add another layer of joint compound and let it dry overnight. Smooth the surface with fine-grade sandpaper and repeat the process a third time if the surface is not yet smooth and even.