Inquiry & Lecture
Different teachers use a myriad of different approaches and styles. As they say in Buddhism, there is different medicine for different people (inner/outer situations).
One way of grouping the styles is in inquiry and lecture. Some teachers use mainly inquiry. Others mainly lecture. And many use a combination of both.
For me, the inquiry style is much more comfortable now. In a pure form, it takes the form of asking a question to the participants, and then everybody - including the main teacher - responding from immediate experience. This can be a wonderfully open-ended, fresh and invigorating exploration, performed individually yet shared with others.
Here, in this shared exploration, the teacher only takes the role as someone (hopefully) more experienced with the terrain (as it appears to her/him), more experienced in describing it, and who has educational and people skills which helps others explore it for themselves. Depending on the setting, she/he may also work more individually with the students and help them see, work with and move beyond wherever they are stuck at the moment.
Of course, it is essential that variations are encouraged. The terrain will not be the exact same one for each person, and their experience of it will also vary. For each person, what they find will have a particular flavor, and they will have their own way of expressing it. This encourages sincere inquiry, and adds to the richness of the overall process and for each individual.
A good example is how the teachers at Kanzeon Zen Center now use the Big Mind process. Instead of giving regular dharma talks, they facilitate the participants in the Big Mind process - and in looking at a particular topic together.