I want to take private dance lessons, but I don't know how to judge how good a teacher is or how much training and education in dance she has had. Are there levels of competency or achievement that I should look for? Are there certificates of achievement that are recognized. I am in South Florida and it seems that every gal and her sister is willing to charge to teach, but I would like to know how I can go about choosing one and deciding if her rates are in line with her experience.

Sometimes it's best to forget about "certificates" or competition results. There are some very good teachers who have never taken an exam, and some "certificated" teachers who have never been on a competition floor.
Instead, take a good, long look at the teacher's other students - is THAT the kind of dancer you want to be? Is that how you want to look? Talk to those students and find out what they say about their teacher.
If competition is your goal, then attend a competition and look at the results of the teacher's students - that can be (but is NOT always) a good indicator of the teacher's capabilities.
Hope you find a good match!

Agree 100%.

Certification only proves a person could pass a test; whether or not they thoroughly know the material they were tested on, or are able to actually impart this knowledge onto a student with results is a different question.

You can pass a college course with full credit with a grade of "C" or better. If I graduated with an A average and someone else graduated with a C average, we'd both have the same certification in our field. Our knowledge of the material would be vastly different, however.

Having gone through a top-notch university and graduate school, I agree in principle with what you say. But that really doesn't help me. I was hoping to learn what various governing bodies evaluate dance teachers and how they signal their evaluations. I was hoping to get some solid answers so I would avoid doing all the legwork myself.