How can a non-EU citizen move to Iceland?
If you are not from an EEA country, you need a residence permit before you travel. It is usually based on one job offer, a study place, or a close family member who already lives here. Útlendingastofnun (the immigration office) decides. Coming first and applying later is the mistake that costs people the most time.
The type of permit decides everything after it: how long you can stay, whether you can change employer, whether your family can come, and whether these years will later count towards permanent residence.