Measure and buy a set of wooden bending handrails to be used as the railing. It is best to buy a set that is slightly longer than you may need, just in case you make a mistake along the way.
Put on gloves and build a simple steam chamber by placing the bending handrails and the end of a steam cleaner into a metal pipe or stove pipe. Seal off the ends of the pipe with several towels to keep the heat and moisture inside the chamber to soften the wooden handrails.
Remove the hot pieces of wood from the steamer after a few hours and quickly clamp them into place along the staircase. Wear gloves to protect your hands from the heated wood and bend each piece along the curve using a series of heavy-duty metal clamps.
Connect each piece of curved railing permanently with a small amount of wood glue between sections. Clamp the sections together for 24 hours to ensure the pieces have properly bonded.
Drill holes along the underside of the winding railing and the upper side of the stairs using an electric drill. Insert the balusters into the holes and seal them into place with additional wood glue.