The best possibility (although still not comfortable) if you don't have a car and don't want to spend money for a taxi.
Departures from Kalwaria Zebrzydowska: click here. Choose fast bus (marked in red), normal buses are very sloooow.
Departures from Krakow: click here, click on top left (Odjazdy z dworca PKS w Krakowie = departures from PKS bus terminal, on Pawia Street, oposite to main railway station), click on letter "K", choose KALWARIA KLASZT. (Kalwaria monastery): departures on left (wyjazd godz.), arrivals = przyjazd godz.
It takes over 1 hour but in contrast to train you get to the monastery instead to a railway station down in the city = it's faster and cheaper.
Hmm... not my recommendation although it's cheap.
From Krakow Glowny (Main Railway Station) you must get to Krakow Plaszow station first (by train prefferably). Then take a train (only a few daily) towards Bielsko-Biala. Finally get a taxi or a bus from the railway station to the sanctuary. It takes... at least 2 hours! - 36 km (22.4 mi) by a car.
Check your train timetable: European timetable.
Kalwaria Zebrzydowska is located in southern Poland, 36 km (22.4 mi) southwest of Krakow, 14 km (8.7 mi) east of Wadowice - birthplace of pope John Paul II and 37 km (23 mi) southeast of Auchwitz (Oswiecim) - former Nazi concentration camp, memorial and museum now.
drive 16 km (10 mi) southwards Highway E77 (direction Chyzne, Zakopane), take exit (turn right) to Highway 96 (direction Wadowice, Bielsko-Biala) to Kalwaria Zebrzydowska. Turn left (follow the direction sign/table on left, easy to miss) towards the sanctuary.
drive eastwards Highway 96 (direction Krakow)
From Auschwitz (Oswiecim):
drive 10 km (6 mi) eastwards Highway 950 to Zator, continue 13 km (8 mi) Highway 950 southwards to Wadowice, take Highway 96 (direction Krakow).