You can easily buy a SIM card at most shops; signing a contract is not obligatory. It is also possible to change your operator without changing your number. If you want to have a contract, and you are not a Polish citizen, you have to get a Polish residence permit first – Karta Pobytu (Temporary Residence Card). However, it is a long process. It might take several months for you to receive your TRC, so in order to have a mobile number in Poland you should buy a prepaid SIM card at first. In most telecom stores you’ll find an English speaking assistant to help you find the best option for you.