It's been quite some time since this thread received a post but here's my two cents:
The GRE (general and specific exams), LSAT, MCAT, GMAT, etc. are all questionable when it comes to measuring a student's potentials in an upper echelon learning environment. That said, it's still required (in most cases) and should be taken seriously (most schools use these test to award scholarships).
I took the GRE general and the GRE specific (Biology). Based on my experience and those of other graduate students I've conversed with, unfortunately I would say that the best way to study for the quantative/qualitative sections is to just put in the work and learn as much as you can. However, for the quantitative (math) section, you'll probably want to focus on the basic rules in each math subjects (Alegbra, Geometry, etc.). Examples of basic rules are shape formulas (triangle, circle, etc.) and theorems (e.g. pythagorean). As for the qualitative, focus on words that sounds the same but means different things (e.g. coral and correl and write and right). Remember that there is no 'failing' grade for the exams as you'll be competing with other students but there is a 'preferred' score (usually over a 1300 for the combined quantative/qualitative sections and a 5 or higher for the essays).
As for the essay section, here's a tip that seems to help most test-takers (myself included). Memorized about 50-100 'big' words (big as in uncommon words, not necessarily long words) and then use as many of them as you can in the essays AND then combine many of the sentences into longer compound sentences. It seems like the essay graders REALLY like long compound sentences with 'big' words. With all things equal, an essay that uses simple sentences and 'small' words will be significantly graded lower than a sentence with many compound sentences and 'big' words EVEN IF THE SUBSTANCES ARE EXACTLY THE SAME THING.