If your thermostat is newly installed and the cooling worked with the previous thermostat, check the following:
1. Verify that the thermostat is set to cool and is calling for cooling, usually indicated by the words "cool on," a snowflake icon, or a shimmering snowflake icon. If the room temperature is below the cool set point, the thermostat display should indicate a call for cooling
2. Confirm that the circuit breakers are on. If you also have a gas furnace, make sure the switch on the furnace is turned to On and the furnace door is closed.
3. If you installed the thermostat yourself, ensure that the wires are matched correctly and securely connected at the thermostat. If there are not separate wire connections to R and Rc on the thermostat, those terminals need a jumper. Some models use a small metal jumper and other models have a switch that needs to be set to "R".
If the same issue occurred with the previous thermostat, then the problem is most likely with your air-conditioning equipment. Call a professional HVAC contractor if the above steps don't solve the issue.