Contact your locality's clerk's office to see if you need any special permit to build the railing. Some jurisdictions require a building permit for this type of work. Also inquire if there is a code regarding a mandatory height of railings in your area. Plan accordingly if you need to make any adjustments per request of your local building department.
Place the 4-inch by 4-inch railing posts at the lowest step on the set of stairs. Use a pencil to trace the bottom of the post where it will fit into the base of the stair. Lay the post aside and cut along the traced lines with the jigsaw. Insert the post into the hole and make sure sits level. Drill two holes on top of each other into the post with the power drill on the side furthest away from the steps. Slip the carriage bolts in the holes and secure them in place with a washer and nut.
Use a clamp vice to affix a 2-inch by 4-inch or 2-inch by 2-inch board to the post. The size depends on how thick you want the railing. Use the measuring tape to measure the distance from the rail to the second staircase. Clamp the top piece of the railing to the wall where the steps stop. Make sure the height distance between the final thread on the stairs and the railing is the same as the distance of the railing to the second step. You can gently mark a line on the wall to help record this measurement so you know where the board needs to be attached.
Using the 2-inch by 4-inch board for a more precise measurement, draw a line on the inserted post so you can cut the post to fit the railing. Use a handsaw to cut the correct angle of the railing using the line you drew on the post in Step 3. Make a small groove in the post's top so you can have a joint in between the stair railing and the post. The groove can be made by drawing a line where you want the groove to be. This should be the height of the railing. Use the router tool to cut the groove into the post.
Place the rail on the post by aligning it with the groove. Use the power drill to make a hole in the wall where the rail ends and where you line was drawn in Step 3. Affix a lag shield into the hole so the lag screw will be secure. Align the railing with the draw line and secure it with the lag screw.
Attach the rail to post using glue and a nail gun. Cut the rest of the smaller rails that stand vertical to their prescribed height. Place no more than two rails per step. To secure them to the handrail, apply glue to both ends and use a nail gun. Use a level to make sure they are straight with the steps. Sand the railing and smaller rails as well as the post and add a polyurethane finish.