Start looking for an apartment as soon as you know where you'll be living. Often the best way to locate a place is through word of mouth. Also check rental listings in the newspaper and on college bulletin boards. The Yellow Pages may list real estate agencies that will help you locate housing but there may be a finder's fee for the service. Be sure you know in advance whether you or the landlord will be expected to pay this fee.
Moving into an apartment can be costly. Often you will be required to provide, up front, the first and last month's rent and a sum equal to one month's rent as a security deposit to be set aside to cover any damage to the apartment while you're living there.
Be careful not to get locked into a long-term lease. They are difficult to break if your plans change. Be aware that if you do try to break a lease you may lose your security deposit.
Consider purchasing renter's insurance. It is fairly inexpensive (about $100/yr for $10,000 coverage) and protects you in the event of theft or fire.