The AC contactor (relay) and start/run capacitor(s) (see illustration below) fail most often and are inexpensive. So it's a safe bet to buy and install those parts right away, especially if your air conditioning service unit is older than five years. The condenser fan motor can also fail, but it runs about $150 — hold off buying that unless you're sure that's the culprit.
Your contractor will do a load calculation to determine the proper central air conditioning unit for your home. This calculation accounts for the climate, size, shape and orientation of your home, as well as its square footage. A professional will also look at the insulation, windows, walls, floors and other materials that compose your home. He/she will then examine any leaks, seals and existing ducts or vents.
Installation: The old furnace is disconnected from the ductwork plenum, exhaust flue, gas and electrical hookups. In most cases, a new plenum must be made onsite or ordered from a local sheet metal fabricator. A new vent might be required too. The furnace is set and reconnected. Adjustments to the blower fan speed and burner are made to optimize furnace performance for your home and climate.
If you hear clicking that is followed by a hum or buzz, you’re probably hearing the fan motor attempting to start without the boost it needs from the capacitor. You can almost always conclude that the capacitor has failed. Sometimes you can get the compressor fan spinning (clockwise) by pushing it with a thin stick or long screwdriver poked through the grille. But the chances are good that this might work for one cycle, but the capacitor will fail next time the AC goes on. It’s best to replace the capacitor.