air conditioning system stays on even when we turn off our thermostat
Is there a small switch somewhere n the thermostat that says something like "fan" and has positions for "auto" and "on"? Is it in the "On" position? If what you mean is that the fan keeps blowing when the thermostat is not calling for cooling (but the air at that point is not being cooled) that could be it.

Otherwise, look for a short circuit in the thermostat wiring, which would make the A/C think that the thermostat was calling for cooling all the time.

If the latter, and it's too cold in the house, shut off the circuit breaker supplying the a/c with power.