If it is clicking, the ignition circuit is alive. That rules out a good deal straight away, and what is left is short enough to work through in ten minutes at the hob.
Start with the parts you can lift off
Take the burner cap off and look at it. If it is sitting even slightly proud or rotated, the gas is not arriving where the spark is. Caps go back wrong constantly after cleaning, and it is the single most common cause of this complaint.
Then look at the burner ports, the small holes around the ring. A boil-over fills them with sugar or starch that sets hard. A stiff brush and a straightened paper clip clears them. Do not use anything that can break off in a port.
Then the electrode
The ceramic pin beside the burner has to be dry and clean. A wipe after a spill is often the entire repair. If it is cracked, it will spark to the wrong place or not at all, and it needs replacing.
What clicking on every burner means
If one burner is wet, all of them click. That is normal behavior for the shared spark module and it stops when things dry out. If it persists on all burners with everything dry, the module is failing and that is a service call.
What to stop doing immediately
If you can smell gas at any point in this, stop. Turn everything off, do not touch a switch or a light, open a window, leave the house and call Con Edison before you call anybody else. There is no appliance problem worth taking a chance on and no diagnostics here that will not wait.
Everything short of that, we handle. Call 914-527-5055.
