This is a wooden stair building technique that a stair installer needs to master. Typically we attach most handrail transitions mechanically with either screws in the case of miters or rail bolts in the case of handrail fittings. We always use wood glue and if done right, the mechanical fastener is just for clamping while the glue dries, although the fasteners are insurance; they make sure that the glue joint is never stressed. A rail bolt is a metal fastener that has one end with a machine thread and the other end has a wood screw thread. They come in several sizes, but we use the 5/16″ x 3 1/2″ for joining our rails. The rail bolt is screwed into one mating piece of wood while the machine end is slid into a hole in the other mating piece and alignment is checked, glue is applied and nut is fastened and the 1″ hole is covered with a matching wood plug. When the joint is complete, the resulting piece is sanded smooth. The trick is to make sure both holes in the mating pieces are lined up with each other. Some stair builders mark the center lines and use a doweling jig, but I have found that if one takes a 1/4″ or so section of the railing and drill a hole in the center, it can be used for marking each mating piece of rail to be joined. Once the center is marked, typically a 1/4″ hole is drilled for the 5/16″ lag end and a 3/8″ hole is drilled for the 5/16″ machine thread end and a 1″ hole is drilled into the bottom of the rail that accepts the machine bolt so a nut with washer can be inserted, threaded on and tightened.