How you go about cleaning your stove top will depend greatly on how often you use your stove and how long ago it was since the last cleaning. I once new a bachelor who was a bit tardy in stove top maintenance. His approach was to remove the top and take it to the nearest car wash with an honest to goodness steam cleaner used for grease removal on industrial equipment.
Even the high pressure steam wasn’t enough to remove the many years of nastiness that had permanently glued itself to that stove top. Better then any contact cement currently available at your local home center.
Unfortunately his standards were pretty low. He showed his satisfaction with his limited success by yelling Git-R-Done, and headed off to the refrigerator for another cold one. Finding a mystery container in the fridge from who knows when, but that’s a whole other story.
Personal experience has shown me that after a period of time, weeks not years, a brown buildup will develop under the gas burner area where spilled liquid accumulates, and dries while cooking. Simple multipurpose cleaner, and a paper towel or wash rag will not remove said build up.
This is the time for SOS, the soap impregnated steel wool pads. With a little warm water and a moderate amount of elbow grease these little wonders will remove any, and all stains, brown areas, or burnt on crud that you can come up with.
As I’m not a fanatic, even this small amount of effort is something I reserve for my bi-monthly house cleaning. Using a soapy wash rag for daily maintenance seems to provide an acceptable level of clean in most instances.
Similar effort could be applied to your standard electric stove with removable burners. One way to avoid this much effort would be to install stainless steel burner pans under each burner. They could be removed to be cleaned. Some people even wrap these pans with aluminum foil allowing the foil to be disposed of when it becomes unduly soiled.
Glass top stoves with integrated burners are a different matter. SOS pads would permanently scratch the surface. Refer to the owner manual to be assured of using a cleaning product that won’t damage the glass top.
Surprisingly keeping your stove top clean and shiny isn’t all that hard. The effort will be worthwhile and will reinforce to all your friends and relatives that the food you prepare in your kitchen is top quality and properly prepared.