If you are a citizen of an EU member state the only thing you need to have to enter Poland is a valid travel document or a document confirming identity and citizenship (i.e. your national ID). However, if you wish to travel abroad during your stay in Poland it is a good idea to have a passport with you, as it is necessary to visit some of Poland’s neighbours that don’t belong to the EU.
For a stay shorter than three months there are no formal requirements. Your studies will however take longer. For such a stay a registration of residence is necessary. You should register with Voivodship (Provincial) Office and get a Temporary Residence Card for maximum period of two years.