Citizens from Nordic countries do not need a residence permit to study in Sweden. If you will be studying in Sweden for more than three months and you are not an EU citizen, you need a residence permit.
The Swedish Migration Board website provides information about what is required to obtain a residence permit, as well as the possibility of completing an online application for the majority of matters.
Swedish Migration Board website
The Swedish Embassy in Reykjavik does not accept applications or handle migration cases.