Drill two holes through the front side of the newel post at the height where the handrail will intersect with the newel post using a countersink bit. The countersink will allow you to plug the holes and conceal the holes. Space the holes 1 inch in from each edge of the post.
Hold the handrail in place on the back side of the newel post with the help of a friend. Drive one lag screw through each hole in the newel post into the end of the handrail using a screw gun.
Apply wood glue to the end of the wooden plugs. Insert the plugs with the glue end into the holes. Align the grain of the wood plugs with the grain of the newel post. Allow the glue to dry for 24 hours.
Sand the wood plugs flush with the newel post using fine-grit sandpaper.
Touch up the plugged areas of the newel post with matching wood finish using a touch-up brush.