If you are enrolled at a Swedish university or university college you can work in Sweden during the course of your studies without a work permit. You do, however, need a residence permit if you stay for longer than three months. You can read more about residence permits and visas here.
Nordic, EU and EEA citizens are allowed to reside and work in Sweden without a work and residence permit, but need to register at the Swedish Migration Board.
More liberal Swedish labor migration laws came into force in December 2008, making it much easier to move to Sweden for work for non-EU citizens. This also applies to students. If you have received a job offer after you have finished your studies you are allowed to stay in Sweden to work.
More information about working in Sweden if you are a non-EU/EEA citizen can be found here.
And more information about Studying in Sweden can be found here.