One-Way Ticket from Düsseldorf Aiprort Trainstation (this the station outside the airport where you need to take the Skytrain and not the underground terminal station) to Köln Rudolfplatz is 11,90€. Travel time is around 1 hour. You have to buy it at VRR (the regional transportation network for Düsseldorf) or at VRS (the regional transportation network for Cologne) both networks interline. You either take Regional Express 1 to Cologne main station and from there the subway or Regional Express 5 (RheinRuhrExpress) to Cologone Deutz an also the subway/tram. I can't remember if the train station has separated ticket machines from VRR and Deutsche Bahn or if they are combined machines. I guess it is the later, a combined Deutsche Bahn / VRR machine where you select on the display if you want to buy a Deutsche Bahn or a VRR ticket. If you buy via VRR app the single ticket is for immediate use. You can't buy in advance like a day before! This is the standard for public transportation in Germany.