Coincidentally, I removed mine yesterday to give me better access to my icebox.
First pull off the knobs on the stove. Then, unscrew the thumb screw between the burners. The top will lift right off. The burners should be held on with two spring clips each.
If you want to remove the inset part, you need to remove the gas line, then the screws (with nuts inside) around the perimeter.
My cook top was rusty, so I wire brushed it with a wire wheel in a drill, treated it with naval jelly, then primed and painted it with high temperature paint
made for engines. I finished it off by adding a piece of edge trim under the front edge and two rear corners so it doesn't rub the counter top in transit.