I was supposed to share a Google doc assignment with my teacher and I wrote her email address in, but I can't tell whether she can see it. I don't really want to get a missing assignment, is there a way that I can tell if I actually shared it with her?
Yes. Open the document then click the blue "Share" button at the top. It will open a dialog that lists who the document is shared with and lets you share with more people.
If you click the "Advanced" link in this dialog, it will open a larger dialog that gives more details and controls on who you're sharing the document with and what permissions they each have.