If a student, you need a letter from the school where you will be attending.
Some people have been asked for a receipt of payment of the 1st months rent. And COPIES of everything. You really only need the passport and lease, plus copies, but best always be prepared. different clerks can ask for different paperwork!
You will ask them for a copy of the Empadron for RESIDENCIA. For Residency: If you are an EU Citizen you will go to the National Police on C/ Bailen next to the train station. They will ask for all of the same paperwork plus the Empadron and of course copies of all. If not a student they will ask for proof of Health Insurance valid in Spain and proof you have the means to support yourself financially. You will need to get a Spanish Identity Number, N. I. E. they no longer issue identity cards to EU residents as their home countries ID is valid here.
You would choose the Province Valencia, and then and ASIGNACION de N.I.E.
If you are not an EU citizen you need to go to the National Police on C/ Gremis in the neighborhood Patraix. It is far from the center and you will need to take a taxi. You can make appointments online here.
If you have a VISA which comes with an N.I.E. , Spanish Identity Number, you will choose the Province Valencia, and then Toma De Huellas, Expidicion de Tarjeta Follow the steps to make an appointment. It seems like a daunting process but it is much better than it was and should not take too much time if you have all of the proper paperwork.