starts immediately after your graduation and you have to apply plenty of time before graduation date. By plenty of time, I mean the time INS takes to process your application and approve, estimation: 2 months. This is new rule at my university at least, I don't know about other university...
For the students graduated in May of 2002, they have a little liberty at choosing the OPT starting date, but the start date still has to be earlier than July 5th.