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Where to exit
Take the train to Köln-Messe/Deutz. There are several cheap rates offered by Die Bahn: e.g. the Schöner-Tag-Ticket (discounts for 5 persons, but only inside NRW, and only on work-days) or the Gruppe&Spar (drive in groups with at least six persons, discount up to 70%). Also there is Savings fare (Sparpreise). If you're planning to come via train from abroad, simply check the homepage of your national train company.
How to get from from Köln HBF (Cologne Central-Station) to Köln-Messe/Deutz
Depending on where you come from you can just stay seated, for many trains arriving at the central station in Cologne Köln-Deutz is the next stop. be sure to check your train schedule though. If you really have to get out at Köln HBF to take a look at the cathedral, try this to get to Köln-Deutz: Take the S6 or S12. After two or three minutes you will arrive at Köln-Messe/Deutz. Exit there. The tickets for this trip are called "Cityticket 1b". They cost 2,60 Euro, you should have coins handy.
How to get from Köln-Messe/Deutz to the partyplace
Once you arrived at Köln-Messe/Deutz go down to the subway and watch for signs that advertise lines 1 or 9. Take one of these Trains (direction Bensberg or Königsforst)) and exit at Kalk-Kapelle. Exit the station on the right in direction of travel, take a sharp right turn and go straight ahead into the Wiersbergstraße. After a minute of walking you should see an industrial area, where the Abenteuerhallen ("AH" over the entrance) is located.
Another option is to take the busline 150 (direction "Heinrich-Bützler-Straße") and exit at the stop "Christian-Sünner-Straße" right in front of the Abenteuerhallen. The bus leaves every 30 minutes and you only have to get a short trip ticket (Kurzstrecke), which costs 1,90€.