As an EU national, you are entitled to live in Spain for over 3 months if one of the following is true:
you have a salaried position there
you are self-employed there
you can support yourself and your family
you are a registered student at an educational establishment recognised by the Spanish authorities.
In all of these cases, you must still register with the Central Register of Foreign Nationals (Registro Central de Extranjeros), no later than 3 months after arriving in Spain.
Registering with the Central Register
Do this in one of 2 places:
the Register's local office (oficina de extranjería) in the province where you are living
in your local police station (if the Register has no local office in your province)
What you need to take
Passport or other identity document (not expired)
salaried workers - your contract of employment or other proof of your employment status.
self-employed workers - proof of registration in the register of economic activities (censo de actividades económicas) or other proof of your employment status.
not in employment in Spain? Proof of (i) health cover valid in Spain and (ii) sufficient means to support yourself and your family. Pensioners - provide proof of public health cover.
students - (i) proof of your registration in an educational establishment, (ii) proof of public or private health cover and (iii) formal declaration that you have sufficient means to support yourself during your stay.