hitch-hiking :)
probably by bus, but I don't know the prices.
rda.krakow.pl/pl/detale.php
Przystanek: [type in Mielec]
check "odjazdy z Krakowa RDA" [departures from Krakow Bus Station]
choose date [Data] and hour [Godzina]
click: szukaj... [search...]
if want to go by train:
pkp.com.pl
(also in English)