A mage tutor is a high level magic user or a god that is willing to teach their magic or magical specialty. Most tutors do not pick their students, instead, they let the student pick them. All students do go through a series of tests to see if they are able to handle the magical power needed to perform said magics.
There are generally three levels of student in any field of study. Some do not follow these or the names stand for different levels. This is only a basic guideline for those that want to keep as IC as possible.
This is the beginning level. All students start off here. The tests given before actually becoming a student determine exactly how high in this level you will start out. Most apprentices start off at level 3(D&D rules). Some are higher or some actually start off at level 1 and learn everything from the teacher has to teach from the start.
This is the next level and usually the one filled with the most tests to make sure the student is learning and listening. Spells learned, and powers gained in this level tend to increase in strength exponentially with each rise in level. This is also the level that is the most dangerous for any student.
If a student survives all the tests and doesn't get killed by accident, they will achieve this level. A student can not be named a master in their chosen field until their teacher says they are. Most students stay with their teachers for a period of time after being named a master to help out or work to pay off their tutorship. After reaching master level, no one can take on a student of their own until after they have risen four levels. This could take any amount of time to do.