The Internet offers excellent resources for house-hunters. Most major newspapers have an online version with an accommodation section, such as Dagens Nyheter (look for bostad). If you do not feel comfortable trying to decipher the Swedish language, have a look at The Local, a Swedish newspaper in English.
There are many websites dedicated to searching for accommodation. One of these sites is www.blocket.se, a sort of marketplace for several kinds of goods. Scroll down to bostad (accommodation). Another good website, specifically dedicated to the rental market is www.bostadsportal.se. You can view the ads for free. Nevertheless, if you want to contact the announcers you will need to register and get a subscription. You can also try www.andrahand.se (in Swedish).
Information on housing for rent can be found in local and regional newspapers, and from public or private housing agencies, listed in the phone directory as bostadsforetag. However, due to the rate at which housing is snapped up in Sweden, an effective way of finding somewhere to live is by asking personal contacts if they know of anyone who will be vacating their accommodation, and contacting their landlord directly.