Your primary cooling (1st stage) is controlled by the Y terminal on your thermostat. (Or the Y and O/B terminal if you have a heat pump system) In addition, the G terminal is activated to turn on the fan in your home to circulate the cooler air.
Confirm the furnace / air handler door is closed and turned on. Check the circuit breaker to your equipment.
Confirm the thermostat is set to Cool mode and the setpoint (the smaller number at the top of the thermostat display), is set to a temperature lower than the display temp (the larger number in the center of the display).
Confirm the message "Cool On" is solid (not flashing) on the thermostat display.
Confirm your wiring is correct, and the wires have good contact in the terminals (tug gently on the wires)
Using a multimeter, measure the AC voltage between your Rc wire and your Y wire. Your thermostat operates between 20-30VAC, any reading outside this range should be addressed by a Professional Contractor.