My air conditioner won't shut off after reaching the desired temperature. I put the circuit breaker on off so it wouldn't run anymore. What is my next step in fixing it?

I would disconnect a wire(s) from thermostat, if it turns off, likely a bad thermostat. If it stays on contacts could be welded closed on Compressor contactor. I would check voltage to contactor, if 24 volts is not present, unit should shut off.
Does inside and outside unit stay on?

Is it just the condenser unit that won`t cut off? Or is it the inside blower also?