How do I figure out why the thermostat isn’t working in the house for central airconditioning? What do I need to check to get my airconditioning to work?

If you can run your system manually, then you know it's the thermostat that has malfunctioned. If it does not run manually then the fault is in the system or a component to the system. This is generally done by a well trained tech, that has been certified. Let's start with the make and model of your thermostat, as well as your system make and model so we can pull up a troubleshooting guide and diagnose your issues.