【If you are enrolling in further studies at Waseda University】

Depending on your plans, you must submit the "Application for Extension of Period of Stay". See here for the specifics of the procedure. If there is an interval between graduation and enrollment, you must return to your country and apply for a "Certificate of Eligibility (COE)". For the procedures of applying for COE, please make sure to check the information from the office of the department you are scheduled to enroll at.

【If you are scheduled to enroll in Universities other than Waseda】

Submit a "Notification of the accepting organization (leave)" to the Immigration Bureau within 14 days after your graduation from Waseda University. You may submit at their office, through mail, or internet. For further details, see here.
Please inquire your prospective university on the "Application for Extension of Period of Stay".