Staying more than 3 months
Every person who lives in Iceland is registered at Registers Iceland and has a national ID number (kennitala) which is a unique, ten-digit number. Your national ID number is your personal identifier and is used widely throughout Icelandic society. ID numbers are necessary to access a wide range of services, like opening a bank account, registering your legal domicile and obtaining a home telephone.
To apply for Icelandic ID number, you must fill in an application called A-271 that can be found here.
The first six digits of a national ID number show the day, month and year of your birth. Connected to your the national ID number, Registers Iceland maintains vital information on your legal domicile, name, birth, changes of address, children, relationship status, etc.
More information about ID numbers can be found here.
EEA or EFTA nationals that apply for registration in Iceland need to demonstrate their capacity for financial support for at least three months from their registration date. Read more about this here.
As an EEA or EFTA citizen, you may stay in Iceland for three to six months without being registered. The time period is calculated from the day of arrival in Iceland.

If you are employed, Registers Iceland website has thorough information on what to do depending on what applies to you:
Studying in Iceland – Directions on the application process by Registers Iceland.
Assessment of previous education
Going through the process of submitting your qualifications and educational degrees for recognition can improve your opportunities and your status in the labour market and lead to higher wages. Visit this part of our site to read about the assessment of previous education.
You can apply for being registered in the national registry if you are somehow related to or have a close relationship with another person that is an EEA/EFTA citizen, that has a legal domicile in Iceland, and you will be supported by this person.
Directions on the family reunification application process – By Registers Iceland
Au-pair or Volunteer
Those who come to Iceland to work as a volunteer for an approved volunteer organization or stay as an Au-Pair for a family living in Iceland.