I need to share a google doc with my teacher. How do I do that?

To share a Google doc:

Open your document and click on the blue 'Share' button on the top right.
 
Enter the person's email address in the 'Add People' box.
 
You'll see by their name: 'Can Edit'.  That means they can make changes to your paper if you need them to. Click the arrow and you can change their permission for your document to 'Can comment' (they can add comments, but not change your paper) or 'Can view' (They can only see it, nothing else.)
 
If you want the person to receive an email that you've shared the document, leave the 'Notify people via email' checked. If not, uncheck.
Click 'Share and Save'.
 
Once shared, the person will see your document in their document list.