The website for the CAT is at:
http://www.cityairporttrain.com/content/catfacts_EN.php
The bus mentioned above to the Mitte station costs €5,80 each way.
Since all options take you through Mitte, the S-Bahn is very useful unless time is of the absolute essence. As mentioned avbove, take Line 7 from the Airport to Mitte, and transfer to the U-Bahn (U4) for the short trip to Karlsplatz (it's only two stops away from Mitte).
The website for the Wiener Linien (Transit System) is at:
http://www.wienerlinien.at/wl/wlini...e/guestHome.jsp
Route map at:
http://www.wienerlinien.at/WienerSta...WNLOAD/SVP.pdf
Keep in mind that you can purchase a one-day unlimited visitor's ticket for the transt system for €5,- (a three-day unlimited ticket is €12,-)