They come in a variety of forms, done both consciously and unconcsiously; too long to list.
For instance, she may want to test your interest in her. In this case how often you call or ask for a date is factored in her evaluation. How to pass? Don't be too much of a challange. Call her at least once a week and date her at least that much. But, don't call or show too much interest either.
Another test I have encountered is the jealousy test. She will mention other guys that are interested in her and how "hot" they are, etc. Or, if you see her somewhere, she will divert her attention to another guy to guage your reaction. How to pass? Act like it does not bother you at all. The moment you start showing jealousy or possessiveness, you fail the test.
Of course the classic test, I call the "how much will you kiss my ass" test. Basically, she will test your manliness or lack thereof by telling you to do things. If you supplicate, you fail the test.
There are others, but I cannot list them all. The ones above are generally the most obvious ones you will encounter.