Does anyone know how long it take to get from Cologne to Amsterdam by train and about how much it might cost?
Here's two useful websites that allow you to compare and contrast. You can take either the slower, but cheaper national rail lines, or the high speed trains run by the Thalys company:
Actually, the high speed Thalys trains do not go directly to Cologne. You would have to go from Amsterdam to Brussels and then Brussels to Köln. The trip takes over 5 hours with a change of trains in Brussels.
In contrast, the also high speed German ICEs go directly from Amsterdam to Koln {sorry, I originally said to Brussels} in only 2:38.
The Cologne Cathedral is right at The train station and is worth an hour . It took me several visits before I took the time ---I was stupid !! As I recall it is about 2 hours to Amsterdam
The standard 2nd class fare for the high-speed ICE trains mentioned by Lee is €56.60. If you book far enough ahead (up to 90 days allowed) at www.bahn.de, you can get a Savings fare as low as €19. Those tickets are for a specific date and departure time and are non-exchangeable and non-refundable.