Becoming a multi-engine rated pilot is simple as far as requirements are concerned. According to part §61.63, a pilot who wishes to add a class rating must receive the proper knowledge and practical training. When the instructor feels the applicant is ready, he will endorse the pilot in the rating he or she is applying for.
            The basic requirements are:

                        * Currently hold a Private Pilot or greater certificate.
                        * Pass Practical Test
                        * Current Medical

            How many hours it will take to receive your endorsement depends on your ability to learn and execute new procedures. It may take as little as 10 hours to complete or 40 hours to complete. The FAA says under part §61.63 that in order to receive your multi-engine rating, your instructor must endorse you. No required hours, no required instruction hours. For more information about the requirements review part §61.63 in the current FAR's.

Don’t have the current FAR/AIM? Check out this site from the FAA.