Wipe up as soon as possible, so as soon as the surface cools. If you wipe up your appliance after each use, and as soon as it cools, you should wipe down the cooking surface, including burners and grates. The sooner you get to the spills and splashes, the easier they will be to clean. The fewer cleaning products you will need. The less work on your part, and the cleaner your surface will be. Also, remember that grease and food spatters will be significantly harder to clean up if the cook top is reheated, as it essentially cooks them on.
 Wipe with a sponge and a few drops of mild dish soap (liquid). If you use a little bit of your typical dish soap, and clean right after you use the stove top, your job will be much easier. Simply put a couple of drops on a sponge and wipe up the cook top. If the spills and splatters do not come up easily, scrub a little harder.
 Or, use a commercial stainless steel spray cleaner. If you do not want to use common dish soap, your other option is to purchase a commercial stainless steel spray cleaner. This is not necessary, but it does make those tougher stains and spills easier to clean. So, the choice is up to you.but when in doubt, using the product designed to clean a stainless steel cook top is probably wise. If you have sensitive skin, however, this cleaning product may be too strong, so consider wearing gloves.
 Dry thoroughly after with a micro-fiber cloth or cotton cloth, otherwise the residue will cause streaking. Even if there is no food particles on your cook top, streaks will make it look dirty. So, get a streak free shine, and keep your cook top looking as nice as the day you bought it by using a soft cloth to dry after cleaning. It takes only seconds to do this and makes a significant difference in the look and feel of the cook top.
 To remove encrusted or burnt on materials from stainless steel, soak the area with a towel dampened with hot water. This will loosen the material. Then you can gently scrape it away with a rubber spatula. You want to use a rubber spatula so as not to scratch your cook top. Unsightly scratches will make you sad, so ward off this, and don't risk it by using rubber spatula or a fingernail.
 If the stain is tough, use a commercial cleaner. That is what commercial cleaners are made for, but they can be hard on your skin, so be sure to wear gloves, or wash your hands right after.
 Always be sure to polish with the grain.