I just bought a house and I realize that the Central AC is not working. The thermostat works, but there's no air blowing from the vents and the outside unit will not come on at all. What could be wrong? Where should I start?

How do you know the tstat works if nothing is working ?
1st, check all breakers,(furnace/airhandler ) and a/c,(turn them off and then back on)
2nd make sure the doors are on airhandler (if furnace is gas)
3rd, set the tstat to fan/cool, (not auto) ,does the airhandler blower come on?
If this is done and double checked then let us know,, we need the brand names and model numbers of the equipment

Yes, please provide more information once you have check those basics. You will need a voltmeter after that to start diagnosing the problem.