You are probably referring to the 'AT' which is a rotating internship type of thing. The swedes have to do that before they can go into 'ST' (accredited specialist training) positions.
Getting into AT positions as a non-swede is very difficult from what I hear. There is however a 'back-door'. I believe it is called 'vikar laekare'. Individual hospitals or clinics can hire EU qualified physicians as non-accredited residents. Once you have the equivalent time and rotations to an 'AT', you can get your eligibility for specialist training positions evaluated by the socialstyrelsen (national health board).
In past years, sweden wasn't training enough physicians to fulfill domestic demand. As a result, entry for EU trained physicians was possible at several levels (e.g. through the 'vik' backdoor). The hospitals and primary care clinics (vardcentrale) where so hard up for physicians that they would pay for 4 week language courses before people started. In the meantime however, the personnel crunch has apparently subsided. Now, they are much more selective and prefer candidates from the EU space who have a specialist qualification and swedisch language skills.
The webpage of the swedish physicians union might be of help to you:
http://www.slf.se/templates/ArticleSLF.aspx?id=2185
Hiring of physicians is done by the 'landsting' which is sort of a provincial health department. Depending on how desperate they are (== further north), they might still be interested to help you out with the paperwork and a language course. You can find a list of the landstings in the brochure on the slf website:
http://www.slf.se/upload/Lakarforbundet/In English/workinginsweden.pdf
I would start in the north and go south from there. To make it easy for you, here are the links to norbottens landsting:
http://www.nll.se/nodsida.aspx?id=12333
And here is their brochure for AT internships:
http://www.nll.se/upload/IB/lg/pers/informationsmaterial/ATenglish.pdf
And for specialist training:
http://www.nll.se/upload/IB/lg/pers/informationsmaterial/STenglish.pdf