Q: how do i link my computer to apple tv

turn on shared iTunes lib in itunes

and make sure router and firewall on the mac allow the required ports

TCP and UDP ports used by Apple software products - Apple Support

then the Apple TV can access the supported media (only the supported formats read under video and audio formats http://www.apple.com/appletv/specs/)

when your mac is turned on

and from your macs side you can use the Apple TV as remote speaker in itunes and if the mac hardware is new enough you can mirror or extend your desktop to display on the tv using Apple TV (this is blocked for drm media such as dvd and blueray though same as with remotedesktop programs)