You must have been offered a job before you can obtain a work permit. Your work permit must have been granted before you leave for Sweden. If your job is for less than three months, you may print out the decision as the card will not be issued in such a case.
Information on fraud regarding applications for work and residence permits:
The Embassy has been made aware that people in Ukraine have sometimes been in contact with companies in Ukraine that claim to be able to assist in receiving work and residence permits in Sweden. Due to this, the Embassy wants to clarify that applications for residence and work permits are only handled by the Swedish Migration Agency. The requirements for obtaining a work permit in Sweden can be found on the Swedish Migration Agency's website, see the link below. The information that has appeared that only a biometric passport is required to obtain a work permit in Sweden is incorrect. The Swedish Embassy in Kiev cooperates only with VFS Global regarding the processing of applications for Schengen visas. The Embassy in Kiev has no other cooperation with companies or sellers in matters concerning residence and work permits. No company or seller can influence the processing time or the outcome of the decision. For correct information about the procedure and work permit requirements, the Embassy refers to the Swedish Migration Agency's site in the link here
General information about work permits
There are several different kinds of work permits, e.g. for artists, au pairs, berry pickers, visiting researchers, athletes and coaches. For details, read the information on the Swedish Migration Agency website. The website also describes what exemptions apply in the case of certain occupational groups working in Sweden for a limited period.
If you are granted a permit for more than three months, you are issued with a residence permit card. The card is proof that you possess a residence permit. Read more under ‘How to apply’ to find out how you arrange for the card.
You can also find more information about the residence permit card on the Migration Agency website.
If you obtain a permit to work in Sweden a family member (e.g. husband/wife and unmarried children under 21) may be granted a residence permit for the same period of time. If you receive a permit for at least six months, members of your family can also obtain work permits. Family members who are granted a residence permit need a residence permit card (see above).
Read more about residence permits for family members on the Swedish Migration Agency website.