If your air conditioner’s compressor is not turning on, there are several steps you can take to troubleshoot and fix the problem. Here are a few things to check:

Check the thermostat to ensure that it is set to the ‘cool’ setting and that the temperature is below the current room temperature. Also, check the batteries in the thermostat and replace them if necessary.
Check the breaker: The compressor may not turn on if the circuit breaker tripped. Locate the circuit breaker panel and check to see if the breaker for the air conditioner is in the “off” position. If it is, switch it to the “on” position.
Check the air filter to see if it needs replacing, as a dirty filter can cause the compressor to overheat and shut off. Locate the air filter and replace it with a new one if it is dirty.
Check the outdoor unit: Ensure that you do not block the outdoor unit with debris or foliage. Clear away any debris or trim any foliage that may obstruct the unit. Also, check to see if the outdoor unit is level, and if not, level the unit.
Check the compressor: The compressor may be faulty and not working. If you are not comfortable troubleshooting and fixing the compressor, it is best to call a professional to diagnose and repair the issue.

If none of these steps solve the problem, it is best to call a professional HVAC technician to diagnose and repair the issue.

In summary,

Check the thermostat
Check the breaker
Check the air filter
Check the outdoor unit
Check the compressor
If none of the above steps solve the problem, call a professional HVAC technician to diagnose and repair the issue.

Additionally, there are a few other things to consider if your air conditioner’s compressor is not turning on:

Check the refrigerant levels: Low refrigerant levels can cause the compressor to shut off. If you suspect this may be the issue, it is best to call a professional to diagnose and repair it. Tampering with refrigerant levels with proper knowledge and equipment can be safe.
Check for leaks: If there are leaks in the refrigerant lines, it can cause the compressor to shut off. If you suspect this may be the issue, it is best to call a professional to diagnose and repair it.
Check the fan: The fan in the outdoor unit is responsible for blowing air over the compressor to keep it cool. If the fan is not working, it can cause the compressor to overheat and shut off. Check the fan to see if it is working correctly. If it is not, replace it.
Check the contactor: The contactor is an electrical switch that controls the flow of power to the compressor. If the contactor is not working correctly, it can cause the compressor not to turn on.

It’s important to note that if you are unsure what to do or suspect the problem is more serious, call a professional.