For national TV networks, they usually only reference two time zones (Eastern and Pacific) and do different broadcast schedules for the east and west coast. On the east coast you'll hear TV shows advertised as "Watch Ow! My Balls! weeknights at 9:30, 8:30 Central". Works similarly on the west coast.
For big, live events (State of the Union, Superbowl, etc), they usually start those at a time that's a compromise. It'll start earlier on the west coast and end later on the east coast. Usually 7PM Eastern is the time chosen for things like that.
And how do people keep track of that time zone if they're not living there?
Mostly just knowing where they are and mental math. I usually only have to deal with time zones for work, and it's typically:
- The vendor/company has 24 hour contact points, so I just call whenever
- I know the vendor is in Chicago and just subtract an hour in my head from east coast time.
- If I'm emailing them, I don't really worry about it unless I'm setting up a meeting. Then I just let the calendar software handle it.