The cheapest way to get to Auschwitz from Krakow is via a bus from the main Krakow bus station. These buses leave hourly from around 7am...and it's a good idea to catch as early a bus as possible as the visit to the concentration camp can take up most of the day. Another option is via one of the mini-buses that picks up in a number of streets around Krakow. I know this is more expensive than the normal bus, but I can't remember by how much. You can travel by either means and not go close to breaking the bank though.

Take the train to and from Auschwitz. It's much more comfortable than the public bus.