The most obvious sign that there is something wrong with your air conditioner is that it is running, but is not cooling the house. On a central unit, check to see that all the vents are open and allowing the cool air inside. Check the air filter to see if it is dirty. Air filters should be replaced monthly; if they are allowed to get dirty they can cause insufficient cooling and icing of the outside condenser unit on a central system. Low refrigerant may also be a problem, but that is more difficult to self-diagnose. An HVAC technician can check that for you and recharge it if there is a leak. Regardless of the type of air conditioner you have, check the settings on the thermostat and be sure the system is set to "cool" and not "heat" or "fan" if your system has those options.
If your central air system is not running at all, see if it is turned on at the thermostat, the air handler and the outside unit. These all have easy-to-use switches and should all be on. Check the circuit breaker box and find out if any part of the air conditioning is on a circuit that has its breaker tripped. This could indicate an electrical problem, but may have just been a one-time overload. If your system has overheated it may have shut down at the air handler, which means you probably need to change the air filter and push in the reset button on the indoor unit. Check the thermostat to make sure the temperature you have the unit set to is actually colder than the ambient temperature in the room. It sounds obvious, but it happens. If the problem is a major motor or compressor malfunction, the broken part will require replacement and the services of a professional.
If your house is getting too cold because the air conditioner will not shut off on its own, check to see if you have the thermostat set too low. If it is set correctly, you may have the wrong-size unit for your home or room. A central unit or room air conditioner that is too small for your particular needs will have to work non-stop to distribute the cool air to the area. Try closing off some of the rooms in your home to make it easier for the air conditioner to cool the place.
If your system continually blows fuses or trip breakers, it either means the compressor needs repair or replacement or the unit has a problem with its electrical wiring. If it is a compressor problem an HVAC repair technician will need to repair or replace the compressor. An electrical wiring problem could cause short circuits, blown fuses and tripped breakers, and you will need to get a qualified electrician to correctly repair all the wiring to guarantee your system is powered correctly and that there is no dangerous wiring. This problem could be a result of faulty installation or poorly insulated wiring that came with your system. It could also be a problem with the home's existing wiring and its inability to carry the electrical load for the appliance. The electrician will know for sure after checking out the situation.