Well it depends how old we are talking here. For the Apple Cinema Display there have been four different connectors in use since its release in 1999. DVI, ADC, Mini Display Port and ThunderBolt. If the one you have has the Mini Display Port or Thunderbolt then you don't need any adaptor as it will work natively in your macs Thunderbolt port (Mini Display and Thunderbolt use the same connector). If it has DVI you can get an Mini Display to DVI adaptor at the Apple Store HERE.
If it has ADC this you have to use multiple connectors and it gets a little pricey and Frankenstein-ish. I Personally have been using the Apple ADC to DVI adapter with a DVI to Mini Display Port adapter for year on my Mac Mini, it a big unit and takes its own power supply. Because this is now a very old product its also very expensive. There is also a cheaper option that has ok reviews that "may" work. A belkin ADC to DVI adaptor, Though I have no Idea how it would work since the Apple Cinema Display is powered via the ADC from the computer, plus the USB would not work though that may not mater since is USB 1 anyway.
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This is a DVI-D cable so that Mini Display Port to DVI adaptor should work just fine for that. $29 Direct from Apple but you could probably find it cheaper on Amazon.