Buses leave frequently from Katowice's main bus station ( ul. Skargi 1 ) every day starting at 8:00. A one way ticket costs about 9-20zł with the journey taking 60-70mins (prices and times depend on the company). The buses make several stops along the way, and most weekday will drop you off at the Oświęcim train station ( ul. Powstańców Śląskich 22 ), which is 1.5km away. From there hop on local buses 24, 25, 26, 27, 28 or 29 to make the short trip to the museum; you can purchase the 2.70zł fare from one of the nearby kiosks.
Auschwitz I and Auschwitz II-Birkenau are located 3km apart (with the train station strategically between them). Between Nov-Feb there is a free museum bus which shuttles visitors between the two parts of the camp every 30 minutes during weekdays from 10:00 (every 10 mins at weekends), with the last bus being at 16:10 (check upon arrival for schedule). Alternatively, catch a cab for a rich 15zł .
To get back to Katowice, waiting minibus taxis run by Malarek Tour (+48 605 31 50 77) can be found outside either camp - a group of eight would pay about 30zł/person. Otherwise you need to catch a bus from the Oświęcim train station . Again, local buses 19, 24, 25, 26, 27, 28 or 29 make the trip from Auschwitz I to the train station for 3zł . Buses from there back to Katowice are frequent, but the last one leaves at 16:48 Mon-Sun.