Something ambiguous is unclear or vague, like the end of a short story that leaves you scratching your head. But if you're ambivalent about something, you can take it or leave it. Whatever.
Ambiguous is something that is confusing or has more than one meaning. It can be the ambiguous look your ex-girlfriend gives you as she leaves the library, or the ambiguous ending of the movie Lost Highway, where you don't know what the heck just happened. Here's the word in action from the news:
Are there threads you might come back to later, or was that a deliberate choice to leave some things about him ambiguous? (New York Times)
"The election law in New York is written in an ill-defined, ambiguous way," Goldfeder said, adding that he did not believe any laws were broken. (Reuters)
Ambivalent is when you don't hate something, but you don't love it either. Since you feel two ways about it, you don't really care. It's often used to describe feelings, attitudes, and relationships:
Danya, now nearly 14, was ambivalent about leaving, drawn toward being a teenager in New York City. (New York Times)
The time of action is upon us, but I remain ambivalent as to what action I should take. (Challeger Deep)
He was vague and ambivalent on matters of policy. (Blink)
When choosing between ambiguous and ambivalent, consider whether you are describing something that is unclear or vague: that's ambiguous. If it's a fluctuation in attitude or feeling, that's ambivalent. If you're ambivalent about ambiguous movie endings, stay away from David Lynch and stick to blockbusters where the good guys win.