My 9 year old girl keeps looking at people when goes out with us ...i get so embarrased how could i teach her not to do so without embarrasing her too?

Talk with her before: Talk with her about this before going out of the home when it is just you two. This will not embarrass her nearly as much as doing this out in public. It is quite normal for a 9 year old to do what you are describing, and she is old enough to have a good conversation about the topic.

9?: She's old enough to reason with. Gently explain that staring at people makes them feel uncomfortable and self conscious. She'll probably need to be reminded (like most children) so agree to a system that if she forgets, you'll gently touch her shoulder to help her remember.

Embarrased: I like very much that you state "without embarrassing her too." negative reinforcement does not work in the long run. 1) first i would examine why you are embarrassed. We learn to be embarrassed. Are you judging yourself as a bad parent? 2) talk to her about how others might feel when stared at. Put it in terms of them and not her or you.