You can buy prepaid SIM in most kiosks (very small shop; I'm not sure is there english word for that (newsstand?)… pic for reference:
http://bi.gazeta.pl/im/3/10906/z10906793Q.jpg) or buy in any mobile network shop. Four biggest and best known mobile networks are: Orange, T-Mobile, Plus and Play. Their shops (except Plus) are at Królewska street about 3km away at south.
If you're using Orange or T-Mobile please check if your provider has some plans for GSM/Internet, since European Union changed some laws about roaming pricing recently.