While the AppleTV supports AirPlay coming from all modern iOS devices, only the following Macs can broadcast via AirPlay while running Mountain Lion:

• iMac (Mid 2011 or newer)
• Mac mini (Mid 2011 or newer)
• MacBook Air (Mid 2011 or newer)
• MacBook Pro (Early 2011 or newer)

If your Mac is older than this, you're more than likely stuck with needing a cable to get video and audio from your machine to your television.

Enter the $7 Monoprice Thunderbolt to HDMI Adapter. Monoprice build great, cheap cables and adaptors, and since Thunderbolt is backwards-compatible with Mini DisplayPort, you can use it slightly older Macs or some PCs, although you'll need an audio cable, too.