Isolate the reading comprehension issues you most have trouble with. Some people have a harder time understanding the main point or overarching argument of a passage of reading; others find it tough to discern how evidence is used to strengthen or weaken a point of view. Consider testing yourself by doing several reading comprehension test questions. The process of completing these word problems will help you figure out what you need to most work on.
Consider what you're trying to get out of a reading passage. Comprehension doesn't mean memorization. There are a number of different approaches you can take if you're reading something for a specific purpose. If you're reading a passage about a criminal case, you might be better served if you seek to comprehend how evidence and arguments worked within the passage. If you're reading about friendship, perhaps tone and discussion between the characters is more important than picking up on specific facts such as location or the weather.
Mark down important sections and ideas as you work your way through practice reading passages. Focus on the specific words themselves to create your own word problems as you progress. For example, if the author of the passage says a conclusion is "obvious" over another, or that certain perspectives are "negligent and flawed," it is a good idea to jot this down in the margins or underline it. Placing your own emphasis on the words as you come across them is an effective word exercise as it allows you to spot the authors mechanisms on your own, increasing your comprehension.
Rephrase important points and conclusions. After you've read some passages for practice, rewrite some of the core happenings, evidence or arguments in your own words. You can do this with the main point of the passage as well. Consider even rewriting the structure to explain in layman's terms how the passage was laid out. For example: The first paragraph outlines a debate, the second provides evidence for one side, while the third paragraph dispels evidence for the opposite side. The final paragraph concludes that one side of the debate is unequivocally right.
Practice! The more reading passages you read, the better (and faster) you'll be able to comprehend them. Word problems such as marking and rephrasing will greatly assist you, but you won't make any progress if you don't familiarize yourself with a wide variety of reading.