Typical wiring diagram of a central unit. As you can see the transformer is the boss. If it dies then you will have no heat and no cool. So if nothing is happening you should always check it first. If either the 120 v side or the 24v side is open you have a bad transformer. Some transformers are stand alone models while others are incorporated in with the fan relay. Why a relay? Heat side must have a slow speed fan and cool side must have a high speed. So the next thing is to check the relay. That is discused on another sublime page.
Typical 24 volt transformer
Fan relay with transformer built-in
All of these items should be checked for continuity.
If you have a failure of the unit to come on or a fan failure.
The above diagram shows how a system works using
24 volts. The 24 volts allows for smaller wires to run through walls to various inside and outside units so everythang can be all jiggity.