Most modern gas stoves use electronic ignition to light the burners. Turning the knob activates an electric spark which ignites a small amount of gas that lights the burners. The clicking sound you hear when the stove is working normally is the sound of the ignition. If the stove igniter stops clicking, there are a number of things you can check such as the gas delivery system before you make a call to the repairman.
Plug the stove in and check the outlet with a known working appliance.
Set the burners in the "Off" position; remove the grates and lift the top of the stove. Use a straight pin or thin stiff wire brush to clean the holes on the metal tubes that deliver the gas to the burners. Grease and food may have built up, blocking the gas from getting to the igniter. In some stoves, you can lift these elements out, clean them, and reseat them. Check your owner's manual for instructions specific to your model.
Turn off the lights and turn on one of the burners for a few seconds. If you don't see a spark, the igniter module probably needs replacing. Check your owner's manual to find out if this is something you can do yourself or if you need to call a repair person.
Contact a repair professional about replacing the wiring or switches that turn on the ignition, unless you have technical knowledge in this type of repair. If cleaning out the gas delivery system doesn't cause the ignition to work, the stove may have a broken wire or switch. Over time, these parts can fail or become misaligned.
Perform any tests in a well-ventilated room. If you suspect you have a gas leak, leave the area and contact 999 immediately or British Gas (or your gas company) on their emergency hotline 0800 111 999 (This is a 24 hour emergency line).