You would think we all had nuclear reactors sitting in our backyards, with technology so incredibly complicated that the average person could never understand. The truth is it isn't. In fact, every A/C unit out there generally has the same basic parts that make up the unit. Many of which can be replaced by the average person. HVAC people don't want to tell you this, but one of the most popular parts to fail is the electrical contactor.
I've put this repair off for about 3 years, each year I go out and bend, or modify the 18 year old electrical contactor just to get us by. This year it was finally time to replace it. It's actually really simple, and the symptoms of a bad contactor are usually that of an outdoor compressor unit continuing to run after the indoor thermostat is shut off. Other symptoms are the A/C unit not coming on, anal leakage, and a erection lasting more than 4 hours.

A contactor or relay is an electrical device that takes a control signal usually 12 volts DC, 24, 120, 208-230 volts ac and creates a magnetic field to pull in a set of contacts that controls another device that may or may not get its electrical power from the same circuit. Note: 99% of most control circuits are 24 volts AC.
Now here is where things get sticky. You take the top of your heat-pump or A/C unit and find the contactor. You can see the bronze terminals are firmly soldered to the contacts even when you shut the circuit breaker off. The bronze stuff is what keeps the contactor from welding itself shut, and when that wears down, the contactor fails.
You call your HVAC neighbor who wants $150.00 to repair it, and you look up on the Internet how much a part is and they want about $50.00. Or you can just buy it from where the Air Conditioning repair guys get it and pay $10.00.
First look on the coil of the contactor and find it's voltage. Most have stickers, but mine didn't. The voltage should be labelled around the copper wound magnet. If your unsure, almost every major brand home A/C & Heat Pump unit uses a 24 Volt 30 Amp 2 Pole Contactor which can be ordered here for $13.57.
Careful when touching the terminals. Often the the capacitors are still charged and can give you a nice 24volt shock even if the power is cut. I would tell you how to avoid this, but that wouldn't be much fun, now would it?
My new electrical contactor replacement came in less than 2 days, via UPS to the house from MSC's distribution warehouse in Pennsylvania.
Run outside with the bad boy and screw the wires in matching the old positions to the new contactor. Don't be shocked if the contactor looks different. My original 18 year old contactor was definitely "outdated".
While I had the top of the A/C unit off, I pulled the sides of the unit and did some preventive maintenance by cleaning off the leaves, dust, and dog hair on the coil that has been decreasing efficiency and using more electricity.
How to replace a Electo-Magnetic Contactor:
1) Stare and gawk at how an 18 Year old Trane Heat-pump that's never been serviced, still runs.
2) Rip the top off. It's usually just a few screws holding it on:
3) Find the Contactor. Diagnose, and replace:
(There's the new one installed. Much cleaner then the old one... and it works!)
4) Take old Contactor and throw at neighbor's chicken:
5) Go inside and enjoy the cool A/C with the knowledge you don't have to run outside in the middle of the night and smack the unit to get it to shut off!