I also had the ENG described by Lori. I wore a pair of goggles with little video cameras in them, so they could video my eye movements during the tests. In addition to the "caloric" test, where they put warm and cool water in your ears, they did various movements of my head, and some "follow the moving dot" tests. This testing is sometimes called VENG, or Video-ENG.
I had ABR as well, also as described by Lori. The tests are quite useful, they can identify which, if any, nerves are compromised, and how much so. This is useful in deciding whether treatment might be needed, and can contribute to a decision on which kind of treatment.
I will also put in a plug for getting an MRI with contrast. While the ABR and ENG tests are useful, the definitive test for AN is the MRI. Having had both, I was a bit surprised by the costs - the vestibular lab bill was about the same as the MRI bill.
Steve