Look at the stove and ascertain two things: whether it is gas or electric and whether it is self-cleaning. If it is gas, start by removing the burner covers, knobs and drip trays and placing them in a sink full of hot water. Make the water as hot as you can and then add two teaspoons of dish soap. If it is electric, put the reflector bowls in the sink full of soapy water instead. Then spray your cloth with vinegar or kitchen cleaner and wipe down the stove's surface around the heating coils, making sure not to miss the spot below the ring.
Use your steel wool pad to scrub either the burner covers, knobs and drip trays or the reflector bowls. Don't use a knife or your fingernails to try to get off stuck-on food. This will scratch the metal. If any debris doesn't come off easily, leave the item in question to soak for 10 to 15 minutes.
Rinse the items under the tap using warm water. Dry each item with a dish towel or paper towel so you don't leave any spots or streaks. Set them aside on another towel and then remove the racks from the oven. Either soak them in the same water or replace them if they have gotten too dirty. Leave the racks in there until you're finished with Step 4. Spray a cloth with vinegar or glass cleaner and wipe the sides, top and door of the stove. Use the steel wool pad if necessary.
Close and lock the oven if it's self-cleaning and simply turn the knob to the cleaning setting. For an oven that requires you to clean it manually, use either commercial oven cleaner or household ammonia. Either spray the entire surface of the oven with a fine coating of the cleaner, concentrating on the soiled spots, or dip a paper towel into a bowl with two cups of ammonia in it, wring out the cloth, and wipe down the oven. Leave the ammonia in the oven for a half-hour to concentrate on the soiled areas. Then use a cloth soaked in water to remove the ammonia or the residue from the oven cleaner.
Remove the racks from the sink and dry them. Put them back in the oven only when it is cool enough to touch. If you cleaned it yourself, this shouldn't be a problem, but self-cleaning ovens get very, very hot during the process. Finally, put the hardware back on the stovetop and admire your handiwork.