Diagnosis
The cooktop light is housed in a sealed assembly behind a lens cover underneath the microwave. It's a specific halogen bulb (often 50W G9 base) not a standard household bulb.
How to Fix It
Safety first: make sure the microwave is unplugged. 1) Look under the unit. You'll see a clear or frosted plastic lens cover. 2) On one side of this cover, there's a small plastic tab. Gently press the tab inward while pulling down on that side of the cover. It should hinge down. 3) You'll now see the bulb socket. Let the bulb cool completely if it was recently on. 4) Pull the old bulb straight out of the socket—don't twist it. 5) Push the new replacement bulb (make sure it's the correct halogen type) firmly into the socket. 6) Swing the lens cover back up until it clicks into place. Plug the unit back in.
If That Didn't Work
If the new bulb doesn't light, double-check that it's seated all the way in the socket. If it still doesn't work, the issue could be with the light socket or the control board, which is a more involved repair.
Heads Up
Handle the new halogen bulb with a clean cloth or gloves. The oils from your skin can create hot spots on the bulb glass when it's on, causing it to fail prematurely. Also, never use a bulb with a higher wattage than specified.