Scan the Entire Test
Before you spend too much time on one passage, make sure you look over the entire test. Find out how many passages you're going to need to read and look at the number of questions associated with each passage. These exams are usually timed, so you need to make sure you're allowing yourself enough time to complete everything.
Focus on the Questions
It may seem counterintuitive, but you should be reading the questions before the passages they relate to during reading comprehension tests. Checking out the questions will allow you to develop an understanding of what you should be looking for in the passage. This makes it easier for you to find the information you need to pick out the correct answer.
You should also ensure that you're looking at all of your potential answers, especially if the question asks for the best solution. This sometimes means that there are several answers that are almost right. Make sure you pick the solution that is the most correct.
You shouldn't be afraid to skip a question on your first time through the test, either. Go ahead and answer the questions that you're confident about. Come back later and work on digging out the solution to more difficult questions.
Use the Passage
Some reading comprehension questions will ask you to find the definition of a word in a passage. Many times these terms are italicized, so check for that before you spend time reading the entire passage. You can use context clues around the word to figure out the meaning if you don't know it off the top of your head. Similarly, it's usually easy to find the main idea of a passage. Check the beginning and the end of the passage and see if any ideas seem to repeat. This is probably the main point of the piece.
You should also take the time to double-check all of your answers with the passage. If you're pretty sure that one character said something, go ahead and look back to make sure. Don't lose points on something that's easy to confirm.
Additionally, you shouldn't try to limit yourself to only reading the passage one time. Sometimes you're going to need to read it twice, three times, or more to get the information you need. Go ahead and take the extra time to make sure you understand what you're reading. It'll end up giving you a better score in the long run.