Air conditioning thermostat not functioning - Goodman CKL36AR36 Air Conditioner

Go to your thermostat and look at the FAN switch, it will be in the AUTO position typically.
Set the FAN switch to the ON setting,
by doing this if the fan motor operates you know that the High voltage & the low voltage (24 volt control power) are present.
This saves you from having to go to the breaker panel and checking / resetting the breaker as well as checking the Transformer and automotive type 3 amp control circuit fuse (generally on the circuit board).

If you do not get any fan operation by switching the fan switch to the ON setting, you then will have to determine if the breaker, transformer and aforementioned 3 amp fuse are all good.

You will need a volt meter to test further.
At the thermostat remove the cover thus exposing the thermostats sub base and assorted circuits/wiring.

RED or R
Red is the 24 volt "hot leg" of 24 volt power which originates at the transformer. Red enters the thermostat on the Red or R terminal, some thermostats will have an RC and an RH terminal, these are jumpered together on single transformer systems as they are for Red Cool and Red Heat, without a jumper wire on RC and RH, the Red "hot leg" of the 24 volt control voltage will only energize the terminal its wired to, some stats are battery powered and do not use the transformers 24 volt power (parasitically) to power the thermostat.
If the thermostat is powered by the transformers 24 volt power, there will be a "COMMON" wire on the common terminal of the thermostat, this is the other side of the 24 volt power from the transformer, the side opposite from RED the 24 volt "hot leg"
Common is called common as its the side of power that EVERY
24 volt circuit terminates, or completes its circuit, thus the COMMON designation.
During a Heat call the 24 volt hot leg is sent out via the white/heat terminal to the gas valve etc.
So between terminals Common & White , it should read 24 volts during a call for heat.
Same for Fan which is the Green or G terminal,
Same for Cool which is the Yellow or Y terminal.
If you have no power to these terminals when calling for heat or cool or fan then yes the thermostat is defective and requires replacement.
DO NOT let the RED wire touch ground or the COMMON terminal, this is a direct short and blows the fuse or transformer
if not equipped with fuse protection.

Normally you should read 24 volts between RED and COMMON