How can I calm her down and teach her how to greet people. I can keep her on the leash for one thing, but that won't make her less excited. What should I do while approaching the new person? Also how to fix the biting of strangers or even biting in general.
I do not advise leash correction when introducing a dog to a new person. This will teach the dog two things, 1) when the leash is off, I'm free to do as I please, and 2) new people = correction. So I would not follow this advise.
The answer to your question is...what behavior do you want? You need to teach this behavior. The behavior I want with my dog is for her to wait for my instruction while she calmly lays on a mat. This thread with help with teaching calm behavior: http://www.dogforums.com/3-dog-training-forum/2522-doggy-zen.html
When I allow her to greet the guest I want her to sit politely, so teach a bomb proof sit.
Otherwise, and not before you've taught your dog these things, she should not be greeting guests without some form of control. I would employ a crate. If she's too excited, she does not get to greet the guest. I would invite new people over to practice the behaviors you are teaching her. If you see any behavior that you do not want your dog rehearsing, crate her and end the training session until you've done more to teach the behavior you want. Without the ability to give your dog some instruction, you are creating the worst possible training scenario, and this will only leave you frustrated. So teach, practice, teach, practice, have patience, and don't give up.