Usually, the answer is: "Begin at the beginning." But where is that?
A while back, I started a discussion on LinkedIn about useless advice for writing. What topped my list was, "an essay has a beginning, a middle, and an end." Writers may be told the same for novels, and it is really just as useless there because you don't necessarily start with what happened first in the story. In fact, classical works are famous for beginning in medias res. So, there is very good precedent for the beginning of a piece of writing not to lay out the framework to set the chronology.
The key thing is to begin in a way that draws the reader into wanting to continue reading the story, the essay, or the poem. And, yes, you should think of making it interesting even when your reader is also your teacher.
What doesn't work for openers? That question will get different answers. Today someone, no doubt thinking of Bulwer-Lytton posted the warning not to open a novel with the weather. As some pointed out, though, there are novels that do it quite effectively. I would say that there are no set rules for opening novels, and that's a good thing. The perception that there are rules for opening essays, in my humble opinion, is what leads to very formulaic and boring openers, like the one I just read this morning. It started with "The Oxford dictionary defines... ." Now, that is the sort of thing I expect students to rely on -- in high school. It's something they should get beyond in college. Certainly, it's not what I'd expect to find in a piece written by someone who gets paid for his work. It's true that you do sometimes want to use a formal definition to clarify how you use a particular term, but it's not exactly an attention-grabber.
Any thoughts on what you find does work well for openers?