Position the stair posts on the stair treads at the top and bottom of the stairway, and then trace around the posts. Drill holes at the four corners of the tracings and cut along the lines you traced, using a jigsaw.
Slide the posts through the holes in the stair treads and place a torpedo level on each post to ensure they are plumb. Drill holes through the side of the staircase and into the posts. Insert bolts through the holes you drilled, securing a washer and nut on the ends of the bolts, located under the stairs.
Secure the railing to the top and bottom posts using clamps. Adjust the railing so the bottom edge sits 36 inches from the stair treads. Use a pencil to mark where the bottom edge sits against the posts.
Remove the clamps and the stair rail. Cut the posts along the lines you marked, using a handsaw. Lay the rail over the posts and drive nails through the rail and into the posts, securing it in place.
Measure the distance between the stair treads and the bottom of the handrail, which should be the same measurement at each stair tread. Measure the angle of the handrail by holding a carpenter’s compass against the bottom of the rail. Cut balusters to the same length, trimming the tops at the same angle as the handrail sits.
Insert the balusters between the stair treads and the handrail. Drive nails through the underside of the stair treads and the top of the handrail, into the balusters to secure them in place.