A truly fascinating bit of astronomical history.
A working model of a possible version of the intricate mechanism, made by Michael Wright (no known relation to our Chairman) of the London Science museum can be seen on >>>YouTube<<< . The mechanism even catered for the eliptical orbit of the moon mimicking how at times the moon moves across the sky faster than at others; and, how it could follow the Saros, Metonic and Callippic cycles of the sun to predict solar and lunar eclipses. Truly amazing!
Geoff also explained how more recently x-rays and advanced photography methods were used to reveal the true complexity of the device.
These study have facilitated the creation of computer models of how the device worked. You can download videos of an excellent virtual model from www.mogi-vice.com. (NB. you may also need to download new 'codecs' to view the videos).
More information is available from the Antikythera Mechanism Reasearch Project (AMRP) website