The #1 thing I want you to understand: the proficiency hump
Like a lot of my observations, this one stems from frustration.
I've read and reviewed lots of different test-prep books on Amazon.com. Sometimes I'll review a book that I think is mediocre or even (for lack of a better word) crap. For example, I recently read Up Your Score: SAT - a book written by high scoring students - and thought it was just fluff. Then I read some glowing reviews of the same book. My initial reaction was, "these must be fake reviews by friends of the publisher", but then I remembered that for smart, proficient students, almost any prep works.
I think the most important characteristics of a successful test prep student are intelligence, proficiency, and motivation. Let's think about the often overlooked middle factor: proficiency. I'd define proficiency in regards to test prep as having solid foundational skills in literacy, mathematics, writing, and grammar. For tests like the GRE, SAT and ACT, this means that the student reads at or above the college level, is good at arithmetic, algebra, statistics, and geometry, and can write clearly and intelligently.
The more proficient a student is, the easier he can adapt to material on standardized tests... and vice versa. That is probably the #1 thing I want parents to understand. This is why you'll hear all kinds of different stories about what kind of test prep works. These stories may have little or no relevance to your teenager. The prep is one important factor, but proficiency is WAY MORE important. Without proficiency, test prep may be a Sisyphean task for a student. As I've said before, a student's school, classes, and grades may disguise a lack of proficiency in these areas.
The proficiency "hump" that I refer to is hard to exactly define, but it's something I see (to varying degrees) in many of my tutoring students. If someone does not have a certain level of literacy or mathematical knowledge, it may be quite difficult for him to improve despite hard work. Again, the bigger these foundational gaps, the longer improvement will take -- and vice versa.
How do you know if your student is foundationally proficient? Have her take a practice test. It might not give you the complete picture, but it's very good data about what needs to be done next.