You first step will be to measure the location of your railing. Measure from the top of the landing, all the way to the bottom of the stairs and then add 2 feet to that measurement. The rail material you need purchase should be this length.
Some other items you need to get are 90 second epoxy, a 2×4 (about 4 foot long) and some brackets for your handrail. You will need two of them at the top of the stairs, one every 4 feet along the rail and one at the bottom. Now, you are ready to go buy your railing. There are different varieties to choose from, some are oak, pine or poplar. You can shop around for the best buy, to help save yourself some money.
When you are ready to begin installing your rail, you will need to locate your studs with a stud finder and mark them, about 3 feet above the stairs. Then, you will need to cut your railing to the proper length. To do this, you will want to use a miter saw to cut a 45-degree angle on one end. Rest this end on the floor and lay the rail down on the stairs and mark where the railing is touching the top stair. Now, cut a 16-degree angle at the mark you made on the railing. Make sure the rail joint fits and then cut a 45-degree angle at the opposite end of your shorter piece.
Apply a thin layer of your epoxy on both rail section ends and hold them together until it starts to set up. Make sure you allow the epoxy to harden for at least two hours, minimum. After it has dried long enough, you can line up your handrail with your marks you made on the wall at 3 feet, then mark under the rail where each stud is. Finally, you can cut some returns and attach them to your railing ends with glue and tack nails.