Prepare a rag that is not rough. Stainless steel is easily scratched and even a very soft kitchen cleaning ball can damage the surface of stainless steel.
Use a microfiber rag. This type of rag works better than lint-free cotton because it leaves less lint on the surface of stainless steel.
Wipe the refrigerator clean with a paper towel. If you want your fridge to be spotless and shiny, clean the surface with a microfiber rag and your most common cleaner, then wipe the fridge clean with a paper towel.
Clean with the grain. You may need to look closely at the grain on your refrigerator, but you can see where it's growing. Wiping against the grain, even with a microfiber wipe, will leave permanent scratches on the surface of the refrigerator.
Use water. This is the least expensive way to clean your refrigerator, but stubborn stains and fingerprints may require repeated scrubbing or a few drops of detergent in the water before cleaning. If you use soap, you'll want to wash the surface with clean, hot water before drying the refrigerator (dry the surface quickly to avoid leaving marks).
Use oil. Any vegetable oil, including olive oil, is fine to use to clean stainless steel. You can also use baby oil; cleaning with oil eliminates the need to dry the refrigerator with additional oil. This cleaning method will leave the refrigerator very shiny.
Clean the refrigerator with white vinegar and water. Pour a mixture of white vinegar and water into a spray bottle and use three parts white vinegar and one part water. Spray the solution on the refrigerator then wipe it down with a paper towel. Vinegar can remove greasy fingerprints very well.
Use a cleaning product. Some people prefer to use products that clean glass and products specifically designed to clean stainless steel appliances.