Spread tarps on all surrounding stair and floor areas near the metal railing. Protect the stair wood under each railing by applying painter's tape around the perimeter of each railing post.
Put on safety glasses and scrub all surfaces of the metal railing with a wire brush to remove loose and peeling paint. Sand any areas of rust, using 80-grit sandpaper until they are as smooth as the surrounding metal.
Put on chemical-resistant gloves and a respirator. Open all nearby widows to provide adequate ventilation. Saturate a sponge in phosphoric acid and wipe all portions of the rail with the sponge to prevent new rust spots from forming.
Wait 24 hours and re-brush the entire railing with the wire brush to remove any additional rust spots.
Open a can of oil-based metal primer and paint a thin layer on surfaces of the railing, using the paintbrush to get into small crevices. Let the primer dry overnight.
Open a can of oil-based metal paint and apply it to all of the railing surfaces, using a fresh brush. Wait an additional 24 hours, then peel off the tape and roll up the tarps.