Mix warm water and several drops of dish soap in a small bowl. Stir the water until it is sudsy.
Saturate the abrasive side of a dish sponge with the soap and water solution. Scrub away any dirt, oil or residue on the brushed nickel. Wipe it dry with a soft clean cloth.
Dampen a microfiber cloth with white vinegar. Rub the vinegar onto the brushed nickel in long, straight passes.
Allow the vinegar to evaporate from the brushed nickel and check for any additional spotting. Perform another application if spotting remains, this time rubbing the brushed nickel back and forth with the cloth.
Clean the brushed nickel once every two weeks using the same process to prevent further spotting and pitting.