hello Jay welcome to Sweden hope you enjoy your stay
there are a few options that you can take
www.thelocal.se (Swedish news in English) has a notice board and discussion board
www.blocket.se there are people looking for flat mates and apartments here. it might pay for you to start by getting a room then start looking for a apartment as this has been proven to be a difficult task
www.bostaddirekt.com you can look for a apartment here
you might need to get the old dictionary out and start getting the dog ears on theme if you are not to familiar with the language
you can also get along to one of the kiwi club events as there is a good community here in stockholm and there is bound to be someone that knows someone
good luck