EU/EEA
To stay in Sweden for more than three months you will need a Personnummer. This is an identification number given to all Swedes at birth since 1947. It will be required every time you go to the doctor, if you want to open a bank account or get prescribed medicines at the chemist. To obtain it you just need to go to your local Skatteverket office (Swedish Tax Agency) with ID and the completed application for residence form .
You will need to have accommodation in Sweden, as your Personnummer will be sent to your Swedish address. The application is relatively straightforward for EU/EEA citizens and refusals are very rare.
Non EU/EEA
Nationals from a country outside the EU/EEA will need a work permit to enter Sweden. An application for a work permit of more than three months is automatically issued with a residence permit application (see work permit section).
Family ties: The notable exception is residence permits granted on the grounds of family ties. Persons with such a permit are allowed to reside in Sweden but not to work. The relevant family ties are current and prospective spouses, co-habitees and registered partners and children under the age of 18. Anyone dependent on a current Swedish resident can apply for a residence permit. This is also the case for children older than 18. You can apply for a resident permit at your local Swedish consulate or embassy. You will need to bring your passport, two identity photos (taken in the last six months) and a complete form “Application for RP, AP, TD and CRS ”, No. 115021.