"The woman drinks with the teacher."
Translation:Die Frau trinkt mit dem Lehrer.
As always in German, the verb takes the second place in the sentence. "mit dem Lehrer" is a group and "die Frau" is one, so you could either say "Mit dem Lehrer trinkt die Frau" (which isn't commonly used) or "Die Frau trinkt mit dem Lehrer".
Besides, as the woman drinks with the teacher, the teacher also drinks with her. But grammatically, the two sentences I wrote above are the correct ones.