Update for UK Nationals as of 6.7.2020 you need to apply for a TIE instead.
For residents from all other EU countries, you can find form EX-18 in the Certificates section of the Library and direct link below.
For a duplicate certificate you should go to the Foreigners Office or Extranjeria of the Policia Nacional in your area. You should not need anything more than the form and valid ID, so your passport and photocopies of the first and photograph page. Proof of address only if you have moved since you first registered (suggest an updated copy of your padron not more than three months old) and need to update data. And pay the ´tasa´ at the bank with the form you will be given. On the EX18 tick the box which suit your circumstances under:
MODIFICACIÓN
□ De datos personales Change to personal data
□ Por cambio de domicilio Change of address
□ Por cambio de Documento de Identidad/Pasaporte Change of ID or passport
□ Otros(especificar) Others please specify (change of marital status, passport or nationality.
Lost or stolen certificates should be reported to the police first. The police report should also be presented with the application.
Some offices however, if you´ve not been a resident for 5 years, so not a permanent resident yet will require you to provide proof you still meet all the requisites of residency and will ask you to provide proof of income and proof of healthcare, just as when you first applied.