I don't 'diagram' per se, but I do write down key things, like a word or two on the main point of each paragraph, and words that describe the paragraphs in relation to each other, usually like 'counter' or 'support' or whatever. I also underlined proper nouns or obscure, jargony words, because they tend to pop up in questions asking what the author did or did not say. It's a pain to sift through large portions of the passage trying to relocate information you need to answer an otherwise thoughtless question, with an answer directly verifiable from the passage, verbatim. I didn't have a particular science for RC, but my approach became fairly uniform as I did more and more passages. It's basically guaranteed that you will need to understand the main point, the various arguments presented, how the arguments are related, and the author's individual viewpoint on the issue(s) he discusses, which may not be explicitly stated, for each RC passage. Maybe some people are good enough readers that they will do well on RC even without focusing on specific things they should be looking for in each passage. Personally, I knew that I couldn't rely solely on reading skills to get me through RC, so I studied it until the section became easy and predictable because I knew exactly which parts of each passage were 'important,' according to the LSAT. This allows you to save time, because you will intuitively skim through obviously unimportant technical rhetoric that you might otherwise get caught up on processing.
I think it's debatable that reading well is helpful in ascertaining the information that RC questions require. Academic reading tends to be fact-oriented, while the RC section is based on your understanding of the author's argumentation in general (i.e. structure, method, view points, etc. ). Most people probably do not read for generic structure in their every day lives, which is why I think it's important to systematically approach RC. The section itself isn't hard, but I know a lot of people who make the mistake of not studying RC, because they thought there was no room for improvement, since their reading abilities were not going to drastically change before the LSAT. This simply isn't true.