If you are a citizen of a country within the EU/EEA or Switzerland, you do not need to apply for a permit to work in Sweden and can start looking for work immediately. You also have the right to set up and run your own company. If you are a Swiss citizen and wish to work longer than three months, you need to apply for a residence permit.
If you are a citizen of a country outside the EU/EEA or Switzerland, you need to a permit to work in Sweden. There are different kinds of work permit depending on where you come from, how long you plan to stay and what kind of work you intend to do. The Swedish Migration Board explains the details.
If you come from a country outside the EU/EEA
If you are already in Sweden and wish to apply for a work permit
Special rules concerning work permits for certain professions and countries