If you are EU citizen you can enter Poland on the basis of your ID document (or other valid document certyfying identity and citizenship).
For stays exceeding 3 months there is the obligation to Registering the Residence in Pomeranian Voivodship Office in Gdańsk: (free of charge)

Wydział Spraw Obywatelskich i Cudzoziemców
Department of Nationals’ and Foreigners’ Affairs
Pomorski Urząd Wojewódzki w Gdańsku
Pomeranian Voivodeship Office in Gdańsk

Address:
Pomorski Urząd Wojewódzki w Gdańsku
ul. Okopowa 21/27
80-810 Gdańsk
room no 1


Office hours:

Monday 9.00-14.00
Tuesday 11.00-18.00
Wednesday 9.00-14.00
Thursday 9.00-14.00
Friday 9.00-14.00

Here you can find the application form:
Application for registration the residence (2.08 MB)


* Application shall be written in Polish
* Application for registration of residence shall be submitted not later than the day following the expiration of three months from the date of entry into the territory of the Republic of Polish
* Application must be submitted in person

REQUIRED DOCUMENTS

• application (1 original + 3 photocopies),
• photocopy of a valid travel document (the page with personal details) or another document confirming your identity and citizenship,
• confirmation of a temporary stay registration,
• documents or written declarations confirming that the foregoing conditions of stay have been met,
• certificate of enrolment for studies/ course issued by University,
• a document confirming medical insurance coverage or rights to avail of healthcare services pursuant to regulations on coordination of social security systems,
• a written declaration that the person has sufficient financial resources to cover the cost of living in Poland