In my experience, LDS missionaries spend more time teaching and discussing, and less time trying to "prove" the validity of their teaching, than other Christian groups. (This is probably an effect of different epistemological emphases between LDS and others. That is to say, since LDS faith is ultimately based on revelation instead of divine books, more time is spent teaching and encouraging someone to seek that divine revelation than trying to prove it from the Bible or Book of Mormon.)
Sometimes, a person requires years of on-again off-again visits with multiple sets of missionaries, attending LDS meetings, visiting with local Mormons, and so on before gaining that witness. Others seem to receive it much quicker. Regardless of how long it takes, when someone decides they want to join the Church, the next step is rigidly fixed. Before being baptized and confirmed, a member of the LDS church -- a more senior missionary (i.e., a missionary put in charge of other missionaries, not to be confused with "senior missionaries" who are older LDS couples) -- has an interview with the potential baptisee. Instructions on how to carry out these baptismal interviews are provided in writing for the missionaries in their general purpose manual, Preach My Gospel (see chapter 12, p.205ff). The interviewing missionary asks specific but open-ended questions about things like their beliefs in God, Jesus as savior, and living prophets, as well as questions about their commitment to live God's commandments. If all goes well, they schedule a baptism in the local ward, where LDS as well as friends and family are invited.
At the baptism, hymns are sung and a few short words are said about baptism and the Holy Spirit. For the baptism itself, both baptiser and baptisee are dressed in white. In the name of the Father, Son, and Holy Ghost, the baptisee is immersed in water. The following Sunday, the person is called up and introduced to the congregation as the newest member of the community, and then hands are laid upon the head to confirm the gift of the holy spirit. Such are the mechanics of conversion in the LDS Church. Beyond this, as Sam Bhagwat illustrates in his story, true conversion or reconversion remains a daily process, to be gained through scripture reading, prayer, study, and Christ-like living and participation in the LDS community of saints.
Ben Spackman has studied Near Eastern Languages and Civilizations at the University of Chicago, focusing on philology and Semitic languages. He has taught various courses in a volunteer capacity for the LDS Church Education System since 2003 and now serves as the Patheos Mormon Portal Manager.