First it wasn’t nearly as confusing or as slow as it seemed it would be so take heart 😊 Although, it does take time and you get to see a lot of the city…
Second, for non-EU family members of EU citizens it’s one form for both NIE & Tarjeta de residencia.

Our situation is: I’m from Australia and married a Spaniard, here in Spain, this year. (My 90 day Schengen visa had already expired and I was advised by a lawyer this was not a problem once we submitted the marriage papers as long as I didn’t travel).

Step one was to make an appointment with the Oficina de Extranjeria. I got one (in Barcelona) for about a week after the wedding.
Note:
1) you can’t request the appointment until after you are actually married
2) get there early as you have to take a number in order to wait to take a 2nd number in order to have your appointment (!!)
3) make at least two copies of everything
4) The office in Barcelona has moved to C/ Murcia 42 (Metro Navas)

I had to present the following:
- a completed EX-16 form (Solicitud de Certificado de registro como residente comunitaria o Tarjeta de residencia de familiar de ciudadano de la Union) + copies
- Libro de Familia + copy
- my passport + copy
- my husband’s ORIGINAL DNI card + copy
- my certificado de empadronamiento
Note: Before going we were told we needed our literal marriage certificate (Certificado literal de matrimonio) but I hadn’t received that yet and it wasn’t a problem.

At the Oficina de Extranjeria they stamped my EX-16 form and gave me a letter stating a date after which I could go to the Comisaria de Policia. The date was approximately one month later.

Step two at the Policia I had to present:
- the letter from the Oficina de Extranjeria
- my stamped EX-16
- my passport
- 2 passport photos
- my certificado de empadronamiento (this needs to be less than 3 months old)

They take your fingerprints and give you a “Resguardo” (small rectangular piece of paper stating your NIE and where to pick up your card in about one month).
** Take a book and some snacks, I was there for about 4 hours (and there’s no toilet in my local office!) ** Also, try not to scream when half the staff go for a coffee around 11am…

Step three - if you want to travel before your card is ready - Autorizacion de regreso. You need this if you intend to travel out of Spain between getting the resguardo and receiving your actual tarjeta de residencia.

Go to a third office (in Barcelona it’s Av. Marques de Argentera, 4, Sala B. Metro Barceloneta)
Present the following - but first you have to pay a 6Euro tax (I got this form at the office when I arrived):
- completed EX-08 form (Autorizacion de regreso)
- form showing you have paid the relevant tax (fill in the form, make 2 photocopies, pay at any bank where they stamp it as paid)
- the Resguardo
- passport + copy
- itinerary or travel tickets

They give you an A4 size certificate stating you are allowed to leave and reenter Spain. You have to carry this and the resguardo with your passport when you leave and reenter Spain.

We got all the forms from http://www.map.es/servicios/servicios_on_line/extranjeria/modelos_oficiales_solicitudes.html (except for the forms for paying the taxes which they gave us in the various offices).

For the Certificado de Empadronamiento go to your local Ayuntamiento with something stating your address (I took a copy of our water bill which is in my husband’s name and a letter from him stating I also live at that address). Ask them for several copies. In Barcelona you can go to the Oficina de Atenci?n al Ciudadano (OAC).

I hope this helps someone else who’s feeling as confused as I was!! Good luck and enjoy the books you’ll get through on the metro and in the waiting rooms!!

Extremely helpful, thanks a lot (bit late though since you posted in april, but anyway!)

Also, here’s another take on the whole thing: http://www.spainexpat.com/spain/information/eu_residency_in_spain_for_eu_citizens_and_their_family_members/.

Wow, both of those posts are very very helpful! I?m still slightly confused though, I might have missed something…. do I still have to go get my own NIE first from the office near Barceloneta?

No, the NIE is done at the same time as the residence card and the card will arrive with your NIE printed on the front.

thanks for all ur posts.It was really very helpfull.

But there r some changes.

If u ve ur date of wedding,u can make ur appointment for the ministery aswell on;
http://www.map.es.coz to get the appointment takes arround 5 weeks.

what to bring with u onur appointment;

-ur pasport(not neccery copied whole first pages r enough)
-pasport of ur partner(also only first pages r enough)
-empadriomiento(con vivencia is an idea,they see who live onthis adress)
-residencia of spain
-1 foto(DNI size)of the one who applies for the tarjeta
-Libro de Familia(not whole copied just first pages)
-marriage certificado.

make sure that u r there(when ur appointment is early)arround 8.30
coz the line is long.

when u r inthey give u a number
and after calling ur number
u get again a number(they start exactly 9.00)

Hi,
thank you for all the informaion above, it was extremely helpful. Now, if you want to travel before you get your tarjeta de residecia, there are some changes.
The office where you can get Autorizacion de Regreso has moved from Av. Marques de Argentera 4 to Calle Mallorca 213 (metro Diagonal).
Also, they changed the application form number-it is modelo ex13 now. You have to arrange a date before you go there (cita previa!) on this site
http://www.mpt.gob.es/es/servicios/extranjeria.html 
here you can find all the forms and lists of documentation needed for any procedure. Also you can save yourself some time by downloading the payment form (tasas) and pay the tax at the bank before you go to the office.