Get a multimeter and trace the power signal back - starting at the thermostat, then the furnace, then to the unit outside. If there’s no power coming from the thermostat, that’s the issue, etc.

If the power is flowing to the unit check the capacitor. It’s a pretty frequent issue and a pretty cheap part ($25-30 at Grainger). It’s a simple fix, unplugging a few cables and a few screws. Make sure you find the system reset switch after you switch it out. I have a 13 year old unit and my capacitor has gone out twice. It’s the most common problem, and very easy to fix.