To proselytize is to try to persuade someone to switch to your religious beliefs or your way of living. If you are going to proselytize, try not to be too pushy!
The word proselytize can specifically refer to religious evangelism, as in: "Proselytizing is a fundamental component of Mormonism." 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.