EU/EEA students can enter Croatia with a valid ID card or passport and do not need an entrance visa/student visa.
Non-EU/EEA students coming from a country that has a visa-regime with the Republic Croatia need to apply for a visa via the Croatian embassy in their home country before departing for Croatia.
The list of countries whose nationals need a visa to enter Croatia: https://mvep.gov.hr/services-for-citizens/consular-information-22802/visas-22807/visa-requirements-overview-22879/22879
Residence permit
All exchange students who intend to stay in Croatia longer than 90 days need to register at the Central police station if staying for more than 3 months to regulate the Residence Permit.