Mild detergent, (dish washing liquid) and cloth.
For cleaning that needs more power, mild detergent and warm water can do a great job without damaging the stainless steel. Make sure you rinse the surface thoroughly to prevent staining and spotting. Towel dry to prevent water spots which can be caused by minerals in water
Stainless Steel Cleaner.
If you’ve had staining or scratching, or need to polish your stainless steel, a stainless steel cleaner may be a good option. Some of these cleaners and polishes can help minimize scratching and remove stains. They also can polish stainless steel surfaces nicely. Read the directions on the stainless steel cleaner and test in an inconspicuous spot
Depending on the surface finish of your stainless steel, abrasive cleaners can cause scratching. Duller finishes probably won’t show scratching as much as mirror or highly polished finishes. When in doubt, test in a hidden spot, and also work from the least risky type of cleaning, (ie water) to the heavy duty stuff.
Do not forget to rinse.
Gritty or dirty water, or residue from cleaning solutions left on a stainless steel surface can stain or damage the finish.
Do not use cleaners containing chlorine.
While it may be second nature to bleach everything, stainless steel and chlorine don’t mix. Stay away from the bleach when you clean stainless steel.
Do not use steel wool or steel brushes.
These products leave little particles in the surface of the steel and inevitably these particles begin rusting and staining the surface of the steel.
They also can excessively scratch the surface of your stainless steel.
Do not assume it's the cleaner.
If you do have some spotting or staining, and you've followed all of the rules, it may not be the cleaner. Water, especially hard water, can leave spotting and staining on stainless steel surfaces. Towel dry after rinsing can end the problem.