Baby newborn

When your baby is born in Spain, you have to register him/her in the "registro civil".
Apart from this, you have to ask for the "libro de familia" (a little booklet that indicates all the members of the family, including your newborn child).
And, as a national of your country, you have to register the baby also in your Embassy and ask for a passport for him/her.
And finally, in addition to all this, you have to apply for the first TIE card for your baby. (It will be a TIE card, with the lovely picture of your baby.) This procedure is explained in this link.