As a citizen of an EU member state, the only thing you need to enter Poland is a valid travel document or a document confirming your identity and citizenship (i.e., passport or your national ID).
If you stay in Poland for less than three months, there are no formal requirements. However, for more extended stays, you need to register your residence with the Voivodship (Provincial) Office. You will find all necessary and up to date information here.
For non-EU citizens, two documents are required when entering Poland: a valid travel document (passport) and a visa.
As a non-EU Citizen, in case your stay in Poland exceeds three months, you will need to apply for a Temporary Residence Permit to the local Voivodship Office. Remember, you should apply for the Temporary Residence Permit when you are legally staying in Poland, which means after you arrive and before your visa expires.