Purchase round-handrail mounting brackets from your local hardware store. Use a ruler to mark the wall or deck railing at the height you would like to install the handrail. Installation height may vary with code requirements and site applications. When installing a handrail along stairs, mark the desired height along each step to create a diagonal line.
Measure down 3/4 inch from the top of the handrail mark, using a ruler, and mark the level that will be the top of the mounting brackets with a pencil. Draw a line to mark this height across the entire wall. When installing at each stair, the line will be at a diagonal.
Find the framing studs along the entire length of the wall, using a stud finder. Mark those locations at the height of the mounting brackets. Use a drill to place the round rail mounting brackets every 32 inches along the desired rail length, aligning the top of the bracket with the previously marked bracket line. If installing along deck framing, mount the brackets to the exposed deck posts.
Place the round rail in the mounting brackets and secure according to the manufacturer's instructions. Some mounting units may require screw installation to fasten the railing to the bracket while some may have a clamp that locks around the railing. Some systems may also require the use of adhesives.