Identify the type of passage you are presented. Is it an excerpt from a novel, a persuasive essay or part of a scientific paper? If the text is preceded by an short description, read that to find clues. Getting some context on what you are about to read will make comprehension easier.
Skim the text: Read the first and last sentences of the piece, along with any section subheads. Look for words in bold or italicized font. If you are presented with a table of contents, read that.
Quickly read the questions that correspond to the passage. If taking a multiple-choice test, don't bother to read your options yet. Get an idea for what kinds of information you need to gather while reading.
Read the passage, keeping the following questions in mind: Why did the author write this? What point does the author attempt to make make? What style of writing does the author use?
Highlight important portions of the piece as you go and jot down notes in the margins. Perhaps you won't need to refer back to these notes, but writing as you go keeps you focused on the text and much more likely to remember what you just read.
Take a quick pass through all the passage questions. If you know an answer right away, circle the correct answer or write it down. The easiest points come from "What's going on?" questions, that basically ask whether you were paying attention.
Answer the questions that require you to go back into the text and look for the correct answer. This is the time to refer to those notes you took while actively reading.
Leave yourself time to mull over questions that cannot be answered directly from the text. These questions often refer to the author's intent: "What do you think the author meant by--" or, "How do you think the author feels about--" You need to understand both the letter and intent of the passage to answer these correctly.