As of today, WAW has an airport link to town, several trains a day run from the airport terminal to the three main stations and beyond.
http://katowice.gazeta.pl/katowice/1..._na_lotnisko__A_my_wracamy_do.html (article in Polish but with some pics)
This is very good news and long overdue... and just in time for the Euro 2012 Cup. The most important in my opinion is that you now have a more reliable way to get there in rush hour. Not sure how happy the taxi drivers are though.