Except some smaller villages, everywhere the phone is, there should be internet available. Unfortunately cost of it still belongs to highest in Europe - from 30,40 to above 100zl, for a month, depending from the speed. In addition long time contract is mostly required (min. 1 year).
There's more and more free hotspots in Poland. Typical place is the hotel, good restaurant, marketplace in the city, etc., so like in the other countries.
Here's a list of free hotspots in polish cities, although not full surely: hot.spots.pl/index.php?action=szukaj
just buy a umts card. 3g is all over the place
It may be one of solutions.