Inside OS X 10.8 Mountain Lion GM: AirPlay Mirroring
The new Displays pane
Using AirPlay Mirroring on supported Macs with Mountain Lion is very easy: simply pull down the AirPlay menu and select the local Apple TV you want to mirror your display on. The options are populated via Bonjour, just as they currently are within iTunes. This quite a lot more obvious and discoverable than on the iPad, where you have to double click on the Home button and swipe to the right to find AirPlay controls (below).
The default Menu Bar options for Displays now focuses on AirPlay options, rather than the old fashioned "detect displays" and manually setting a resolution. Below, the simpler menu of Mountain Lion (right) compared to today's Lion (left). On Macs that don't support AirPlay Mirroring, this menu simply offers only to open the Displays pane in System Preferences.
Apple has also updated the Displays pane in System Preferences in Mountain Lion, even for Macs too old to support AirPlay Mirroring. Rather the offering a selection of resolutions (as today's Lion does, below top), Displays now simply defaults to the resolution "Best for built-in display," although you can manually select a non-standard resolution by clicking Scaled.
Using AirPlay Mirroring on supported Macs
You can readily identify a Mac that supports AirPlay Mirroring because it gets the AirPlay icon in the Menu Bar (and its drop down options are different too).
Once AirPlay Mirroring is initiated with a specific Apple TV unit from the Menu Bar, the Displays configuration automatically changes to the resolution "Best for AirPlay," with an option to turn on Overscan correction (usually only necessary if you're using an older CRT television; most modern flat panel displays won't cut of portions of the display because of overscan). Note that brightness controls only have an effect on the built in display.
You can manually select a different resolution from Displays, or select the resolution you want to mirror from the AirPlay Menu Bar pulldown, picking either This Mac or the name of the Apple TV you're mirroring the display to from the "Match Desktop Size To:" options.