The folllowing instructions assume that your Apple TV is up and running, and is regustered with iTunes. If this is not te case, you'll have to resort to finding and matching model numbers as other posters have inicated. It also applies only to the 1st Generation Apple TV (the silver one).
In iTunes 9 or higher, select the Apple TV that appears in the devices list. There is a capacity bar that shows you what space is used for what media type, but it also indicates the space remaining on the drive. From that, you can deduce the size of the Apple TV's internal hard disk.
--tonza