Some troubleshooting wants a familiarity with electrical wiring; so if you are not comfortable with either high or low voltage electrical wiring, do not endeavor these techniques. As a substitute, procure the help of a professional HVAC service technician.
When your air conditioner stops working, the first thing you should do is check the most apparent problems, starting with the power. Go to the electrical panel and find the breaker for the air conditioning unit. Turn it to the OFF position, and then reset it back to the ON position. Your breaker may have been tripped but not automatically switched to the OFF position. Resetting it in this manner will get the power running again. Conversely, if when you turn reset the power the breaker sparks, pops or trips to the OFF position, there is a harsher electrical problem. Only a professional HVAC contractor will be able to adequately remedy the problem. Leave the power in the OFF position and call in the pros.
If there is nothing wrong with the electrical, move on to the next step in troubleshooting your air conditioning system. Check the outdoor air conditioning unit and scrutinize the secondary breaker inside. This breaker may need to be reset. There may be a red reset button on the peripheral of the outdoor unit. If the unit has power, try pushing this button. You may need replacement fuses, depending on the model of air conditioner you own. If the problem doesn't lie in either of these electrical instances, move on to the next step.
If the outdoor unit has power, and the power is running correctly from the electrical panel, there may be a problem with the low voltage circuit. Check to make sure the outdoor unit's wires are in good shape and have not been gnawed by bugs or animals. A transformer either located at the outdoor unit or at the indoor air handler powers the low voltage circuit. Again, it is important that a certified and licensed HVAC service technician perform tasks that have to do with electricity and wiring, especially if the homeowner has no skill or knowledge in that area. The transformer will have to be inspected for continuity using a volt-ohms meter.
If you are still having trouble with your air conditioning unit after performing all of these tasks related to the electrical wiring, you should contact an HVAC service professional. There will need to be tests done on the refrigerant levels and the circuitry of the unit that an average homeowner can now do on their own. If your air filters are clean and your electrical service is normal, the issue can only be resolved by having a qualified HVAC specialist inspect and repair the air conditioner.