Watch this video from This Old House to learn how to install a handrail.
1 Stand 4-foot level on first step and hold it plumb.
2 Mark the level where it meets top of second step.
3 Calculate height of handrail and mounting brackets; mark bracket height on level.
4 Use level to mark bracket height on wall at top and bottom of staircase.
5 Snap chalk line to connect the two wall marks.
6 Using electronic stud finder, mark wall studs at top, middle and bottom of staircase.
7 Drill 7/64 inch-diameter screw pilot holes on chalk line and into studs.
8 Screw the mounting brackets to the wall studs.
9 Cut handrail to length, mitering the ends to 45 degrees.
10 Glue and nail a mitered return to each end of the handrail.
11 Prime and paint, or stain and/or varnish the handrail.
12 Once dry, screw handrail to mounting brackets.