Take a GRE practice test. You can purchase books of practice tests or download one from the ETS website.
Analyze your test score. Take note of which questions you answered correctly and which ones you answered incorrectly.
Familiarize yourself with the types of reading comprehension questions. These questions fall into five main types. Some questions ask you to identify the function of a particular word in the passage. Others ask you to find a piece of information from the passage. A third type of question focuses on applying the author's arguments or examples to other situations. Information that isn't explicit in the passage but is implied or stated can also be questioned. Lastly, the test may ask you to describe or identify elements of the author's argument or style.
Practice reading passages. There are two benefits to this. First, if you speed up the time you spend on the passages, you will have more time to study the questions. Secondly, since you know the question types in advance, you will be able to read them looking for the type of information you'll be tested on. The reading comprehension section is all about reading for context; it's the context of the piece that often distinguishes a wrong answer from a right one.
Practice some more. Familiarity with the questions isn't going to come at once, but if you practice regularly, you'll feel it developing.