1. You should start the corresponding administrative procedure at the Spanish consulate in your country of origin or residence, where you will need to apply for a visa as someone eligible for such an exemption.
2. UPF will provide you with an official document, signed by the vice-rector for Teaching Staff, containing the clauses that appear in your employment contract with the University, to be submitted to the consulate along with the other documentation required (criminal record details, medical certificate, etc.).
3. You should obtain notification of having been granted a visa from the consulate within a month, and must enter Spanish territory while the visa is valid (a period of no more than three months). 
4. If you receive authorization for more than six months, you must apply for a foreigner ID card (TIE) within a month of arriving in Spain. To do so, you will need to make an appointment.

More information.

Exemption renewal

Exemptions can be renewed online or in person (by presenting the relevant documentation at any official registry, preferably the Foreign Nationals Office). This procedure can be carried out during the 60 days prior to the expiry of your current exemption. Under no circumstances can an exemption be renewed more than three months after expiring.