Measure and note the distance between the transverse centers of two adjacent fenceposts. Transfer that dimension to a 2-by-4-inch plank and mark the plank. Rest the marked plank on the table of the chop saw with a 2-inch edge held firmly against the saw's guide fence. Trim the plank. Repeat to cut the other rails that will be installed between the same two fenceposts. Privacy fences taller than 48 inches typically require three evenly spaced rails.
Lay the trimmed plank on a flat surface with its 4-inch surfaces horizontal. Screw two coated screws about halfway through each end of the trimmed plank, through its 4-inch surface. The screws should be evenly spaced, about 1 inch from the trimmed ends of the plank. This simple step will make the job easier, especially if you are installing the fence without the help of an assistant.
Measure and mark the first fence post where you intend to install the rails. Align one end of a rail to the transverse center of the post. Using a drill and driving bit, attach the rail to the post by screwing in only one screw. Move to the adjacent post, where the opposite end of the rail will be installed.
Raise the unattached end of the rail and position it on the corresponding fence post. Rest a carpenter's level on the top of the rail. Adjust the position of the rail so it is level. Screw the rail to the fence post with both screws. Return to the first fencepost to secure the rail with the remaining screw. Repeat to cut and attach remaining 2-by-4 rails.