While cleaning greasy stove tops may be intimidating, it's actually quite easy if you have basic cleaning supplies on hand. Most, but not all, gas and electric stoves have a hinged top that lifts up. Always lift this, if your stove is so equipped, and check underneath; there may be extra grease and debris down at burner level that needs to be cleaned as well.
Fill a spray bottle with white vinegar.
Wipe away all loose residue and debris with a damp cloth.
Sprinkle baking soda over greasy spots.
Spray the vinegar on to the baking-soda covered greasy spots. It will bubble---this is normal. Let the vinegar and baking soda sit for about 5 minutes, longer if you know the grease is especially stubborn.
Go over the stove top with a clean rag again. This time most of the grease should come up; the baking soda will help to absorb it and also scour it off.
Pour a capful or a generous squirt of Joy dishwashing liquid into the sink, then fill the sink with hot water. Use this mixture to wipe down the stove, as it will cut through any remaining grease. If there is stubborn grease that still won't come off, wipe on a generous layer of soapy water and then let it sit until the grease comes off when wiped again---this may take anywhere from 5 minutes to an hour.
Soak greasy stove reflectors, if your stove has them, in the sink while you're busy wiping off the top of the stove. The Joy will help loosen the grease from the reflectors, too, so once the top of the stove is clean, you can just wipe the reflectors off and put them back on the stove.