The round piece of metal visible in the center of each of your stove's burners is part of the stove burner assembly. These parts do not need to cleaned as often as the surface of your stove, but an occasional cleaning will help to prevent clogs in the burner assembly that can cause it to stop working. Cleaning a burner assembly only takes a few minutes and there are no expensive or unusual tools or cleaning agents needed.
Unplug the stove from the electrical outlet and make sure that all of the burner dials are in the "off" position. You do not need to shut off the gas, but burner dials left on will leak gas into the room while you work.
Lift the top lid of your stove to reveal the burner assembly. Most stoves have supports at the sides of the hinged lid or in the center front of the lid to hold it open.
Lift the burner assembly straight up and completely off the stove. Most burner assemblies pop right off; if yours does not, look for one or two small screws holding it in place on either side--these are shipping screws used to hold the stove together during transit and can be removed and discarded.
Scrub at the openings of the burner assembly with a wire tube brush to remove any clogs. Do not use water to clean the burner assembly, just use the brush to scrub away any debris clogging the opening.
Wipe the surface of the burner assembly with a rag that is slightly damp, if necessary to remove debris. Dry the burner assembly with a clean towel.
Place the burner assembly back on the stove. You may need to wiggle it a bit to line it up correctly, but it should snap back into place easily.
Close the lid of the stove and plug the stove back into the electrical outlet.