To proselytize is to try to persuade someone to switch to your religious beliefs or your way of living. "Like a true evangelist, Amber proselytized about the rewards of life as a devout adherent of the faith."
The word proselytize can specifically refer to religious evangelism, as in: "Proselytizing is a fundamental component of Mormonism, with mandatory mission work." Proselytize, however, can also be used for any situation when people are trying to convince others to try something or to join something. TV ads proselytize about the pleasures of life with mouthwash, friends proselytize about how great their favorite video games are, and moms proselytize about the benefits of eating vegetables.