Anyone who's ever used a stove knows how disgusting it is to clean up, particularly when you're dealing with the grease coating the burner/grates. Sure you can buy fancy grease remover, but Vivienne of the V Spot blog has an even better method that involves using a large ziploc bag and a cheap bottle of ammonia to make the process a little easier.
Take about 1/4 cup of ammonia and seal it up with one of the burners in a large ziploc bag. The idea is not to soak the burner but to seal it up with the ammonia fumes. Just in case the bag leaks and causes a stink, you might want to place it somewhere safe outdoors overnight. After about 12 hours of sitting, take out the burner and wipe clean with a sponge before rinsing.
Warning: Never mix ammonia with anything that has bleach to avoid creating toxic fumes.