For more information about requirements for EU/EEA citizens see "Residence Permit for EU/EEA-citizens".
With the Swedish Migration Board's electronic applications you can on-line fill in and send applications, enclose passport copies and other attachments and pay application fees. Family members to the main applicant can apply at the same time – one application per family. link http://www.migrationsverket.se/english.jsp
If you are not a citizen of an EU/EEA-country you must have a work permit in order to work in Sweden. Once you have been granted a permit, it must be entered into your passport before your arrival.
Obtaining a Swedish work permit is no easy matter. Swedes, foreign citizens already living in Sweden and EU/EEA citizens have preference over others in obtaining work in Sweden.
If the offer of work is for more than three months you will also require a Swedish residence permit.
If you will be in Sweden for less than three months, you will not require a residence permit. You may, however, require an entry visa. Information about which citizens are required to have entry visas and more information on visas is found on the page 'Visa for visiting Sweden'.
Requirements for a work permit
Your residence permit must be entered in your passport before your arrival in Sweden.