There are several different reasons that this may be happening a few things that you can check before calling in the experts. First, try checking all your air filters - if they are dirty, go ahead and replace. Next, locate the electrical panel box for the house and check the breaker for the Air Conditioning. If the breaker for the unit is tripped, try and reset it. It is not normal for the breaker to trip, so even if this resets the unit you still should get the unit checked out.
If your air conditioner is buzzing or humming and not running, it likely has to do with an electrical component. It may be the contactor is "pitted". There may even be some loose wires. Knocking sounds can be a sign that there is an issue with the compressor. Even if the unit is working properly, have a professional look at it to avoid future major issues.
Most modern furnaces do not have a pilot light. If you have an older furnace that still uses a pilot light, it is strongly recommended to have a qualified professional look over the system.
The clicking noise is your furnace starting up (igniting). If you hear more than a couple clicks, it's best to call a professional because there may be a deeper lying issue. Even if your heat is working, the excessive clicking is an indication of a future failure.
Not all furnaces have an ignition spark system. Some use hot surface igniters that have no sound.
Changing your filter regularly is the most important maintenance for your unit. Ground mounted outdoor units need to be kept clear of debris, clutter; weeds or landscaping that can grow too close and reduce the airflow to the unit. Also, keep pets away from the unit because pet urine can cause expensive damage. Use caution with a weed trimmer around the unit to prevent damaging control wiring. Any additional maintenance should only be performed by qualified personnel.
Your HVAC systems should be serviced before the start of each heating and cooling season. So, your air conditioner should have regular maintenance performed at the end of winter or beginning of spring, while your heat pump or furnace should have its regular maintenance performed at the end of summer or beginning of fall.