The following three businesses sell lists of rental housing. The Voice is out in newspaper stands every Friday. The Express is free and comes out Thursday afternoons. The West County Times has rental listings, most in Contra Costa County to the north of Berkeley. The University-focused Daily Californian is published daily when the University is in session.
Residence halls are available to the public during summer vacation with advance reservations.
Another resource for students is the University Students' Cooperative Association. USCA is a non-profit organization that houses 1300 students in 20 units close to the Berkeley campus. It is a low-cost alternative that has been in existence since the Great Depression. The YMCA has short-term housing. Best wishes in your move to Berkeley.