Look for foaming around the A/C unit. Liquid may have flooded back into the compressor and caused failure. The refrigerant often foams in this instance, indicating a compressor failure.
Listen to the air conditioner as it runs. The fan will run as soon as the machine turns on, and the compressor should switch on shortly thereafter. The compressor typically turns on and off at regular intervals while the machine is running. Listen for the added hum of the compressor. If you only hear the fan, the compressor isn't turning on properly and may have failed entirely. Unusual noises coming from the system's outside motor also indicate a compressor problem.
Check the breakers if the A/C unit shuts off and won't restart. The system may have overheated or caused a short due to the compressor failing, and it tripped the breaker to shut down the system. If the breaker is regularly shutting off, a faulty compressor is a likely culprit.