After the person wishing to become a Jew has completed their studies (1-6 years on average), they go before a Rabbinical court. The convert goes to mikvah (a ritual bath [not the same as baptism]). Male converts also have to undergo circumcision. If the person is already circumcised, there is a symbolic circumcision where a drop of blood is drawn.
Judaism does not proselytize or seek converts, but it does accept sincere converts. Conversion is a life-changing and very serious undertaking and a potential convert should think it over carefully. It must not be done on a whim or because of temporary circumstances. One who converts is expected (from then on) to live as a Jew.
The first step would be, without outside help or influence, to get to know about Judaism. The person who felt interested should hang around a Jewish community in order to get a sense of whether Jews and Judaism as it is actually lived appeal to him/her. Also to do some reading. English-language books on Jewish thought and life can be found in Hebrew bookstores.
After that, the interested person would approach a Rabbi and ask about enrolling in a relevant formal course of study. This can last for several years and is an integral part of the process, since he/she will have to actually practice the religion.
Once that is completed, the convert immerses in a mikveh (ritual immersion); and, for uncircumcised males, undergoes circumcision.
