If you are a citizen of the Nordic passport union (Denmark, Faroe Islands, Finland, Greenland, Iceland, Norway and Sweden) you do not need any kind of permit or registration to live and work in Sweden.
If you are a citizen of the EU/EEA and are staying for less than three months in Sweden, you do not need a permit to live and work in Sweden. You can start working without registering at the Swedish Migration Board. If you want to stay longer than three months, you must register to continue to be legally resident in the country. This is granted to students, employees, self-employed, service providers and to those who have sufficient funds to support themselves. The certificate will be extended to EU/EEA family members.
If you are a citizen from a country outside the EU/EEA you will need a work and residence permit. For those who already have a permanent residence visa for an EU country or Switzerland, the entry requirements are similar to EU/EEA citizens.
In other cases you will need to obtain a work permit and, if you are planning to remain more than three months, a residence permit will also be required (this will be delivered along with your work permit). To obtain a work permit you must have an employment offer prior to your arrival in Sweden. The job you are applying for must have been advertised in Sweden and the EU for at least ten days and the terms of employment must be equal or better than those customary in Sweden. The relevant trade union must also have had the opportunity to review the terms and conditions and the monthly wage must be equal or superior to SEK 13,000 (~ € 1,265) before taxation. The fee for a first application is SEK 2,000 (~ € 194), for its extension (if the employment and terms do not change) the fee is SEK 1,000. The permit is either valid for the duration of the temporary employment or for two years. After 48 months of employment in Sweden, the holder is eligible for a permanent residence permit.
The work and residence permit must be obtained from outside Sweden and be attached to your passport before your arrival to the country. There are some exceptions, notably for students who have completed a number of postgraduate credits and who want to work in the country. Exceptionally, candidates present in the country for an interview can obtain a permit, if employment starts immediately and if there is high demand in the sector.
If you obtain a work/residence permit, your family will automatically receive a residence permit for the duration of your stay. In this case, your legal partner and your or his/her children under the age of 18 are considered as family, or if your child depended on you just before you left for Sweden (for more see residence permit section).
For more information about your situation, take a look at the Swedish Migration Board website, which offers a comprehensive overview. You can also contact your local Swedish consulate for information relevant to your specific case.