You'll need the permiso de circulacion (Vehicle registration document).
ITV (cert of roadworthiness)
Receipt for vehicle tax
The above are provided by the seller
Personal ID (NIE, Passport) of both buyer and seller
Transfer of Ownership document (Solicitud de Transmisión de Vehículos) which has to be signed by the buyer and the seller. You also need to draw up a sale agreement with the seller which shows the date and time the vehicle will be transferred (in case of any fines at a later date).