An NIE is simply a identification number issued to you by the government and need one to buy a house or a car, and numerous other things. It stays with you for life.
An application form
The Tasa (a fee, which is €9.20)
Passport (and photocopy of passport)
Where you apply for this varies depending on where you are. It can be Orihuela, Torrevieja, Elche or Alicante city, if you are in the Alicante region. If you come under the Murcia region, then you must go to Murcia City or Cartagena.
If you are in Orihuela, Elche or Alicante we have to make an appointment (usually 2 weeks away), but the NIE is issued on the same day.
In Torrevieja, no appointment is needed, but you will need to make a return visit to collect, which usually takes a week.
If you don't fancy battling with this yourself, you can PM either Macanna or Something Silly and they offer a service to assist you in sorting out the paperwork.