While you don't need a Visa to study in Spain, if you're from the EU, you will need to register for a Certificate of Registration, which will confirm your right to study in Spain, at the Central Registry Office for Foreigners. This will be valid from 1 year from the date of issue, so you'll have to renew it every year you're studying in Spain. As an EU student, you'll be required to show a valid passport (or national identity card) and proof you've been accepted onto a university course to get a certificate.
However, if you want to rent somewhere to live or get a job then you will also need a NIE (Número de Identificación de Extranjeros) which is an ID number required for EU citizens who are planning to stay in Spain for over 3 months. You can apply for an NIE at either the national police department or the Oficina de Extranjeros (Department of Foreigners) in the city, in Spain, which you're living in. This process may take between one and five weeks and you will need:
- An application form (an original and a copy)
- Your passport with a photo
- The address where you're currently living
- The reason for your move to Spain (studying!)
On top of these, you will need to prove that you are enrolled in a Spanish university, have sufficient income to support yourself financially without needing income support and have comprehensive health cover, which you will have if you're under 28 because you'll be covered by a student's insurance fund.
You'll also need a thorough knowledge of Spanish and be able to prove you're proficient through an exam of some sort. However, if you're studying in a area with a local language, such as Catalan in Catalonia, you'll also need a knowledge of this language, however a lot of universities provide language courses for international students.