Black Madonna in Poland

Polski Bus is very inexpensive, especially if you book ahead...just plug in "Kraków" and then "Częstochowa" and check the bus station location relative to the monastery. It looks like a 2 hour and 40 min trip. Alternatively, you can rent a car...it's not difficult to drive in Poland. The most expensive option will probably be a guided tour.
http://www.polskibus.com/en/index.htm

Its on the way between Warsaw and Krakow, so I'd consider doing it as a stop on the way, rather than a day trip. It was very crowded when we were there, so don't count on an in-and-out visit. It was a shuffling line, with tradition being that part of it should be on your knees.

Thank you for the info. If you disembark the train, do you pay again to continue to WAW? also if there a luggage storage at the station?

Below is the train info, I'm fairly sure you'd have to pay for two individual segments. But I wouldn't worry, train fares in Poland are inexpensive compared to Western Europe, so it's not a deal breaker if you have to pay for two trips (especially since it will be cheaper than a separate day trip round-trip fare, unless you get an inexpensive bus ticket). You may have to e-mail someone to ask or Google a Trip Advisor Forum on the train station amenities. I went there by car, so I have not seen the train station.

http://rozklad-pkp.pl/en

Train from Warsaw to Czestochowa can be a bit of a pain as I think you need to get off the train at Kielce and then catch a second train to Czestochowa. I'd have to disagree with a previous poster in that Czestochowa isn't really "between Warsaw and Krakow".

Polskibus is a VERY good option. Very cheap, comfortable and takes around 3 hrs'ish to get to Czestochowa. You could then stay overnight ni Czestochowa at the Patria hotel right opposite the monastery and park. From Czestochowa you can catch a train direct to Krakow.

You can use the portal about Polish trains
http://rozklad-pkp.pl/en