To install a stairway railing, first measure and mark the important places, such as wall studs and bracket locations, mount the brackets, and clamp the rail. After that, cut the ends of the rail, and attach the rail and the returns.
Make marks on the wall at the bottom and top of the stairs, use chalk to connect the marks, find wall studs using a stud finder, and mark them along the chalk line. Mark the bracket locations; use a level to make sure that they are plumb. Place the railing at the correct height along the chalk line, ask somebody to hold it in place, and position the bracket on the wall. Punch holes through the mounting holes of the brackets using an awl, drill some pilot holes, and attach the brackets to the wall. Attach the long rail to the brackets, and position the shorter one using a level.
Mark the angles for the cuts on both rails. Use a handsaw to cut both rails simultaneously. Use a miter box to cut the upper and lower ends of the rail, and then cut the return pieces of the rail. Cover the ends of the rail and the returns with glue, put the returns in place, and secure them with L-brackets and screws. Attach the rail to brackets, secure the connection with screws, coat the top end of both rails with glue, and attach the short rail to wall brackets. Put a metal plate underneath the railing to reinforce the joint.