I had a similar problem a couple of years ago the first time I took the GMAT. RC was defiitely my weak area.
When I took the Princeton Review class prior to my first GMAT, the instructor told me not to read the passage, but to go to the question and then skim to find the answer.
This strategy is totally wrong! RC tests your comprehension, the ability to understand and put information together from different parts of the passage, not just to look up answers in the text.
What really helped me was to read the RC passage with the intent of the author in mind. I would think to myself, "what was the author's purpose for including this paragraph?" I would also take brief notes on each paragraph, which helped me understand the topic better as well as the overall theme. I believe I took about 3-4 minutes throughly reading each passage.
Only after I had read the entire passage would I even read the first question. This is very important as you don't want the question to distract you during your initial reading.
Approach answering the questions by a process of elimination. The answer choices may be reworded or stated in a different way, so make sure you understand the meaning of each answer before eliminating it. Also, pay attention to the verbs used in the answer choices, making sure they fit the theme of the passage. For example, you should be able to eliminate answers to purpose questions just by the first word (argue vs. discuss vs. analyze vs. refute vs. propose, etc...).