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 (say: OOT-len-din-ga-stof-nun, 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.