I love teaching my mother language. Greek is a rich language, and I feel proud when students come to me to teach them!
I teach Greek since I moved to Canada 3+ years ago.
There are many reasons for wanting to learn Greek. Here in Edmonton, my students have Greek parents (one or both). The parents want to continue their language and culture through their kids. Another reason is because of tourism. Many adults and kids want to learn Greek to communicate when they travel to Greece for holidays. Do you want to hear something interesting? A Chinese colleague of mine wanted to learn Greek sometime in his life because he knows so much about Greek philosophers, and he felt that he should be able to learn a few Greek!
I could say Greek has a medium level in languages' difficulty. Vocabulary is very rich and Grammar, too. Greek is different than other languages. This should not discourage you from learning it. When you know the simple grammar rules to form correct sentences, then it becomes easy language!
History and traditions! If my students are interested in these, I teach the history behind the big Greek national celebrations. My students love asking questions and discussing the various traditions all over Greece (islands, continental areas), foods, sightseeing, etc.
As I mentioned before, Greek is a rich language. Any time you should be able to adjust your teaching material based on the student's needs. That means, if a teacher has five students in one day, she will probably have to prepare five different materials.
Study. As in all courses, the more you study, the better you become! ;)
Vocabulary. My students always ask why I use many words for the same thing. This depends on the situation, the person you talk with, and what you want to emphasize.
Do not give up! If a student is struggling, there is no good communication with the teacher. Talk about what is difficult for you and your teacher will help you with that.
It depends on how much you study and your living environment. A student who studies a lot and lives in an environment where somebody speaks Greek will be fluent in less than a year. This does not mean that if there is no one speaking Greek, the student will not become fluent. The more you study, the less time you need to achieve your goals.