People who practice Buddhism do not formally convert to Buddhism, but instead take precepts as a way of solidifying their commitment. It is possible to take Buddhist precepts and continue practicing another religion.
The first level of precepts is 5 precepts: not to kill, lie, steal, do bad things out of lust, or take intoxicants in order to induce heedlessness. Taking 5 precepts signals a serious commitment to practice. A person taking the 5 precepts is given a short bib-like garment (called a kasa) to symbolize this commitment. The 5 precepts are common to all forms of Mahayana Buddhism.
In the Kwan Um School of Zen, taking 10 precepts means that a person has shown maturity in their practice and is ready and willing to help lead practice, help beginners, and give short talks. These people are called dharma teachers in training, and after further maturity and training they are given long robes and called dharma teachers.
Taking 16 precepts means that a person is mature enough to give consulting interviews in which students may ask questions relating to practice, or about how practice relates to their lives. Such a person is called a senior dharma teacher, and few students in the Kwan Um school have this title.
A further level of precepts is an additional 48 lay precepts, bringing the total to 64, the maximum possible for lay people in Buddhism.
Separate from the precepts is inka and transmission. Inka is full authorization to teach, including kong-ans; people with inka are called dharma masters (in Korean, ji do poep sa nim). After inka may come transmission; people with transmission are called Zen masters. In the Kwan Um school of Zen “teacher” means someone with inka or transmission. Every Zen center in the school must have a guiding teacher with inka or transmission. Some of the larger centers have two or even three teachers.