Public transport is quite good in Poland. It is not very expensive, but affordable. Although infrastructure here is undergoing a lot of changes, it is not difficult to get around in order to visit the various cities.
Sprint Air and LOT are the carriers that will connect you to the major Polish cities. Ryanair is a carrier for those travelling on a budget.
The PolRegio train service is excellent for regional travel. Other regular urban rail services can be found in Warsaw, Krakow, Gydnia, Gdansk and Poznan. Tickets for the same can be bought online or at the station itself.
You can travel around Poland in charter buses, which are cheap and also popular for short distances. Every Polish town will have a bus centre which is not difficult to find. You can also rent a car or a cab to drive around. Roads here are divided into categories -- A for motorways, S for expressways and so on.