Wash the stainless spoons with warm soap and water in a bowl or in the sink. Dry them with a soft towel.
Check for stains or streaks, dark spots or rust. Set all pieces aside that do not need to be cleaned.
Place 1/2 cup white vinegar in a bowl and place the spotty spoons in the bowl. Rub the spoons with a soft cloth in the white vinegar and check to see if they are clean. Towle suggests that club soda will work as well as white vinegar to remove heat streaks.
Use olive oil or baby oil as an additional cleaner for spoons that did not come clean with white vinegar. Pour some oil onto a clean cloth and rub the spots on the stainless spoons.
Try flour or baking soda cleaning if the spoons still have spots or streaks. Ohio State University suggests dry flour while Mrs. Clean recommends baking soda for cleaning stainless sinks. Use the flour or baking soda dry or make a paste with water and wipe it gently onto the silverware.
Wash the stainless spoons in hot detergent water to remove all traces of the cleanser before use.