CGN to DUS: The only direct rail connection CGN - Duesseldorf main station is an ICE train every hour ( 40 min ). The same train also stops at DUS airpot rail terminal ( 47 min ). Otherwise you can take the local train to Cologne main station and switch to local/IC/ICE trains bound for Duesseldorf there.

DUS to CGN: You can either take the local train from underneath the main terminal to Duesseldorf main station and switch to local/IC/ICE to Cologne there. If you want a "direct" connection, you can connect to the DUS rail terminal by the annoying "Skytrain" or shuttle bus. From there you get essentially the same train choices as from Duesseldorf main station and the hourly ICE connection to CGN.