Most students at the University share housing, usually from two to four in a house. Be specific about your needs, requirements, etc., and be sure to let folks know that they can call you collect to increase your chances of being called. Another option is to contact the various food co-ops in town. They each have housing sections on their bulletin boards. These have proved to be excellent sources for students at Bastyr University.
Newspapers provide another source.
They publish a joint Sunday paper, available as early as Saturday. On the East side, another daily is The Journal American. Many communities publish weekly newspapers that often contain housing classifieds. Talk to managers of any apartment buildings that catch your eye. Put in an application even if there are not any vacancies at the time.