What's the best and fastest way to get from Warsaw to Krakow?
I would suggest taking a train - express one takes about 2 hours, slower one about 4 hours. You can find the info on the intercity train website.
And there is always a blablacar option. Until now, I met only nice Polish drivers on blablacar, the trips are fast, quite cheap, and more flexible than a train ride (stopping for food or shopping if needed).
By Polskibus.com - the cheapest way to travel in Poland by Bus
or by train
I think the easiest option is to look at PKP railway. There are planty of direct connections between Warsaw (polish Warszawa) and Cracow (polish Kraków), see details on http://rozklad-pkp.pl/en .
Another good option is to take bus operated by PolskiBus. http://www.polskibus.com/en/index.htm
You can also seek somebody going to Krakow on BlaBlaCar car pooling platform https://www.blablacar.pl I advise to use polish version of the site blablacar.pl and not other language versions, for example english blablacar.co.uk, because other versions don't show all the search results, nearly none. That's my observation after searching on blablacar.co.uk which showed only one person going from Warsaw to Cracow. That's not true, it is very busy route.
Catch a train!
The fastest trip is by train. See other answers.
By the train, it takes about 2,5 h. You can check timetable here http://rozklad-pkp.pl/en