Since you specifically mentioned UCLA and USC, both have student housing offices on campus that carry a list of vetted properties for lease. In addition, local landlords post their rentals in the Daily Bruin Newspaper (UCLA) or the Daily Trojan (USC).
My best tip, though, is to contact their alumni offices, tell them you are a new student, and ask if any alumni either have apartments for lease or rent out rooms to students.
Hope this helps...and good luck with school!
Keller Williams Realty
Drive around the Fairfax/Melrose area and call all the For Rent signs posted--the rents are usually reasonable--or better to say--there are some reasonably priced places in the bunch.
talk to other students.