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 blinking) on the thermostat display.
Confirm your wiring is correct, and the wires have good contact in the terminals (tug gently on the wires)
Check your jumper / R wire. Thermostats get power on the R and Rc terminals.If you have a wire in the R terminal, and no wire in the RC terminal, use the jumper selector switch, the jumper plug, or a small jumper wire to connect the R and Rc terminals. If you have a wire in the RC terminal, but no wire in the R terminal, move the wire from RC to the R terminal and use the jumper selector switch, the jumper plug, or a small jumper wire to connect the R and Rc terminals. If you have a wire in the R terminal, and another wire (not a jumper) in the RC terminal, you will not need to connect the R and RC terminals. See our Basic Wiring article for more info here.
Using a multimeter, measure the AC voltage between your Rc wire (or R wire if no RC wire is present) wire and your Y wire. Your thermostat operates between 20-30VAC, any reading outside this range should be addressed by a Professional Contractor.