Add 4 inches to the handrail's finished height. Transfer this measurement to a 4-by-4 inch board and cut the board straight across with a circular saw. Cut a second 4-by-4 board to the same height as the first board.
Notch out a 3-by-3-inch section from the bottom of each board with a jigsaw. Use a 1/2 inch wood chisel to smooth away any rough areas. Test each board against the stair's side that it will rest against -- usually the posts are positioned against the top and bottom steps. Hold the board with the notch side overlapping the stair.
Hold a level against each stair post and adjust it as necessary. Hammer four deck nails through the post to secure it in place.
Lay a 2-by-4 board on the stairs with one side pressed against the two posts. Draw a line down the 2-by-4 board to indicate where the end of each post hits it. Cut the 2-by-4 board along those lines with a circular saw.
Hold the 2-by-4 board along the posts with the cut ends lined up with the posts' ends. Adjust the board so it sits at the correct height above the stairs. Secure the board to each post with four deck nails.
Cut off any post that extends above the 2-by-4 with a reciprocating saw. Use the 2-by-4 as a guide to determine the proper angle to cut each post. Measure the distance between the stair and the board. Add 2 inches and transfer this measurement to 1-by-2 boards. Cut the boards to the appropriate length with a circular saw. These boards are the spindles.
Determine how far apart to mount the spindles -- generally 3 to 4 inches. Hold the first spindle over the first location. Use a pencil to mark the 2-by-4 board's slope onto the spindle's top edge. Cut the spindle along the mark. Repeat with the remaining spindles. Position each spindle at the appropriate location and use a level to make it plumb. Secure each spindle in place with deck nails.
Center a cap rail over the 2-by-4 board. Secure the cap rail to the board with deck nails.