Germany has an excellent high speed train system, and
there are many
trains between Berlin and Koeln. The high speed ones take 4.5 hours
and cost about 100 Euro. The slower ones take up to 6.5 hours and
will be around 85 Euro. You can buy tickets in any major train
station but on the long distance connections you always need to
reserve a seat, and that's done best a few days ahead. Time schedules
and tickets online via <http://www.bahn.de/p/view/index.shtml>.
if you hurry up and book at least 3 days ago, you even can get an extra
discount.
Cheers,
ce