Stainless steel isn't prone to rust, but you may find that items that when rust-prone items are allowed to sit in contact with the stainless steel in moist conditions for prolonged periods of time, or in the presence of additional corrosive elements like salt, rust stains develop nonetheless. Removing these stains is considerably easier with the right cleaning solutions and a tested approach. Try out these methods and materials in a small inconspicuous spot first before using them on a wider area to help make sure that you will achieve the desired result.
Remove all extra objects and loose debris from the stainless steel sink or stainless steel surface that has developed the rust mark. If there are pots and pans or other objects that have rust on them, these are probably the objects that caused the stain and should be set aside for cleaning. Thoroughly wet the area with water. Take a moderate amount of Barkeeper's Friend, about 1 TB at a time. Add just enough water to make a soft paste. Apply the paste directly to the rust stain and allow to sit for 1 to 2 minutes. After two minutes, work on the stain with a clean sponge or non-abrasive scouring pad wet with water. Thoroughly rinse the area with clear water. If some stain remains, repeat the process. When stain removal has been completed to your satisfaction, thoroughly rinse the area with water, paying special attention to whether or not there is any cleaning solution residue remaining. Pat dry with clean dry paper towels. Rinsing thoroughly with water and patting dry with clean paper towels between each use is a good maintenance tip as well. For added conditioning, you can dampen a corner of a clean paper towel or soft cloth with a small amount of olive oil, and buff lightly into the stainless steel surface.
Caution: Never mix cleaning agents or chemicals, the result can be dangerous or deadly. Before cleaning, always test the agent on an inconspicuous location to determine its suitability and to make certain it does not damage the material. Wear appropriate clothing such as gloves and protective eyewear, and work in a well-ventilated area. Accidental inhalation or ingestion of cleaning agents can be hazardous and even fatal, particularly to pets and children.