Cologne is in the western part of Germany and is easily reachable. There are many Airports near by and the main train station is very good connected.
Cologne/Bonn Airport (CGN)
This is the nearest airport a little bit outside from Cologne. It has quite a number of connections within Europe, especially with low cost airlines like Eurowings and RyanAir. There are only very few intercontinental flights, in those cases Düsseldorf and Frankfurt (see below) are the better choices. From there, you'll have various connections with regional trains to Cologne Central Station.
Düsseldorf is also very close to Cologne, with a good train connection to Cologne. Depending on the train you use, it takes between 35 - 60 minutes to get to Cologne Central Station. Düsseldorf Airport has two train stations: "Düsseldorf Flughafen Terminal" is the station for a local train which also goes to Cologne but takes a while to get there (> 60 Minutes), so make sure to take the "SkyTrain" to the station "Düsseldorf Flughafen". From there, you'll have various connections with both, regional (cheeper, but takes a bit longer) and long-distance trains (ICE, IC) to Cologne Central Station.
Frankfurt is the biggest Airport in Germany with connections all over the world. The fastest train connection will bring you to Cologne in under 1 hour, so don't be scared by the large distance between the two cities - you'll be there in no time!
A special hint for those of you flying with a StarAlliance airline: There is a special service between the train stations of Frankfurt Airport and Cologne called "AirRail". With this service, it's possible to book a flight to Cologne Central Station via Frankfurt, where the last leg is a train journey instead of a flight. The service gives you some extra benefits, i.e. a separate checkin area at the airport station, the fact that you don't need another ticket for the train. The airport code for Cologne Central is QKL, so give it a try if you fly with StarAlliance!