Before You Begin

Make sure that your Mac is up-to-date and that the TV in the room that you are trying to mirror your screen to is either AirPlay-compatible or has an Apple TV. You can only do this on the Private WiFi network, so ensure that you are connected to Private. 

Mirroring to an Apple TV

It's a fairly straightforward process, on most Macs, all you have to do is click on the AirPlay icon on the menu on the top of the screen. 

From there, you will select the name of the Apple TV.

If you don't see the AirPlay icon in the menu bar

If you don't see that icon on the top menu of your screen, open System Preferences, then select "Displays."