When traveling between Polish (and not only Polish) cities, two most common options are trains and buses.
Polish train network is quite extensive, though trains differ in cost, speed and level of comfort. To find the most convenient connections, visit the website www.rozklad-pkp.pl. You can buy tickets for some connections online, but it is perfectly common to buy them also at the train station, just before the departure.
Traveling by buses is now becoming increasingly popular, especially because of attractive promotions and discounts offered by Polski Bus (www.PolskiBus.com). It connects many Polish cities, you can book the tickets online (recommended as they sell out very quickly) and if you buy them in advance, you can get the prices for even 1 PLN.
Other options for traveling around Poland are hitchhiking (free and relatively safe) and BlaBlaCar (www.BlaBlaCar.pl).