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GRE reading passages range from those written for the educated layman to those written in a very academic style - a style meant for other academics. You're not going to have any trouble with the easier passages, so I want to give you a few thoughts about the more difficult ones.
I'm going to start with the exhortation that you start reading academic journals in a variety of areas. Many of my science students need to explore the humanities more, and my humanities students often need to read more science. By increasing your background knowledge of a topic, you naturally increase your comprehension for it. The passage about the cathedral in the Official Guide is a good example of a passage than can be made easier if you know some architectural language.
Next, consider academic structure. I'll give you a few examples that are common:
Informative passages generally are written to elucidate something or someone. A good example is the passage about Wanda Landowska in the Verbal Reasoning Practice book. Notice the writer's opinion in that passage is not contrasted with anyone else's.
Opinion passages generally advance the writer's point-of-view about something. This opinion is often contrasted with others' opinions, so that the writer has context for her views. Check out the long passage in the Official Guide to the Revised GRE in the 2nd paper test about people's migration, for example. Notice that the writer begins with some background information, presents one viewpoint, then asserts his contrasting viewpoint.
Natural Science passages often present a new finding, which is often written about in the context of what was known prior to the new discovery. These passages sometimes end by discussing the implications of the new finding. The "iceberg passage" in the first PowerPrep2 computer test is a good example of this passage type. The writer begins with background info, describes an experiment which reveals something new, then discusses the implications of the finding.
Of course, there are exceptions to these tendencies. But the main thing I want you guys to start doing is to start recognizing the structure of a passage. Not only will you directly be asked about it with some questions, but it will improve your ability to work with any passage.
Finally, for long passages, read for gist. I personally have the attitude that "if I don't get it, I don't need to get it". In other words, if I don't understand something, I keep moving and focusing on the big picture. If I read a detail I might not remember, I move past it and keep focusing on the big picture.
At the end of the day, all GRE passages are well-written and are by smart people. With some practice, I hope you will feel confident that you can understand anything they might throw at you.