DIAGNOSIS: This is almost always a dead battery in the electronic ignition module. The clicking is the spark generator trying, but there's not enough juice to make a proper spark.
FIX: Flip up the control panel on the front of the grill. You'll see a small black plastic box—that's the ignition module. Slide the battery cover off (it might just snap off or slide sideways). Replace the two AA batteries inside. Make sure the positive ends are facing the right way, as marked. Close it up and try lighting again.
IF THAT DIDN'T WORK: Check the electrode wires running from the module to each burner. Sometimes they get disconnected or the ceramic insulator cracks. Make sure the metal tips are firmly seated in the module and near the burner ports.
HEADS UP: Even with a fresh battery, you still need to hold the knob in for a second or two after ignition to let the flame sensor confirm there's fire, otherwise the safety system will cut the gas.