You can't prepare for the GRE test. In general, the test is a test of patterns, not facts, so if you want to increase your GRE score, you'll need plenty of time to practice. We suggest you spend 4-12 weeks preparing for the GRE. As mentioned earlier, there is a great deal of variation in the amount of time people choose to prepare for the GRE.
However, most people spend between one and three months studying a few hours a week for GRE. This means that the number of studies for GRE could range from approximately eight hours (studying two hours a week for four weeks) to 120 hours (studying ten hours a week for 12 weeks). The average student spends 3 months preparing for the GRE exam. Although it seems like a long time, you will see that it is the perfect duration for this type of test.
Taking a practice test at the beginning of your GRE preparation is a great way to assess what you need to work on. The clear and detailed GRE PrepKhan Academy videos from Khan Academy can be a useful resource for your GRE study, particularly for the Quantitative Reasoning section of the exam. This means that you have a slight advantage in GRE over GMAT, but they are close enough that you can select the test you're most comfortable with (assuming both GRE and GMAT are accepted for the programs you want). I received an email from a university asking me to retake a gre test to meet the minimum requirement.
Many test takers consider GRE to be a much more difficult test than CAT, as the GRE curriculum is more intensive and tests students in everything from verbal reasoning, quantitative aptitude to analytical writing. If you scored 284 for the content and for the strange GRE style, it would be absolutely feasible to see an increase of 15 to 20 points once you've internalized the GRE style and more content. People can take practice tests, read the different sections of the exam, read old school notes, buy and read a GRE prep book or a combination of the above. My Gre test is in 2 weeks and I have been studying for GRE for 3 months, about 2 hours every other day.
Your next step, if you haven't already, is to take a GRE practice test so you can get an idea of how you're currently getting your scores. If you work with math on a daily basis, you'll likely need less preparation in that area, which can reduce the amount of time you need to efficiently prepare for GRE. It's usually pretty easy to know which one (physics programs tend to care much more about the quantitative section, while enlightened programs tend to focus quite heavily on the GRE verbal section), but check with them just to make sure before you devote (or cancel) six months of GRE study that they may not do a difference in your chances of admission. If you're starting more or less from scratch, you might wonder if it's possible to prepare 90-day (~3 months) GRE.