Air Seperation Plant works by using the Joule Thomson Effect to cool the air stream to very low temperature such that air components like Nitrogen or Oxygen will liquidify. The rate of cooling by the Joule Thomson Effect can be increased significantly by using a network of heat exchangers and expanders to cool the air and maintain high pressure such that the Joule Thomson effect can be maximised.
Google for the Linde Process (Single Stage Throttle), Claude Process (Expander), Heylandt Process.