If you are from a country that has no visa exemption with Hungary, you need to apply for a student visa. Useful pages: http://www.schengenvisainfo.com/hungary-visa/
If you are allowed to stay in Hungary for up to 90 days without a visa, you can apply for the residence permit after your arrival. In this case, you need to do the following: Residence permit >>>
For more information on housing: Accomodation >>>
For more information on traveling to Szeged: Travel information >>>