Apostrophe help, please.

The apostrophe is used to indicate possession. A simple "s" at the end of the word indicates plural.

In your example, "teachers" is a plural, so no apostrophe.

Places where you need an apostrophe:

The teacher's chair had a tack on it. (one teacher, 's indicates we're referring to the chair belonging to the teacher)

All the cars were parked in the teachers' parking lot. (The parking lot belongs to more than one teacher so we need to make the word teacher plural with an "s", plus we need to indicate possession with the apostrophe)

One of my teachers. "Teachers" is plural of teacher. That's all. There shouldn't be an apostrophe. Now, here's the fun part:

One of my teachers' pet peeve is note-passing in class.

Is it the pet peeve of one of my teachers, or is it my teacher's one pet peeve? As in:

One of my teacher's pet peeves is note-passing in class.