Looking at the Longman's Writers Companion textbook I noticed a web site listed about "Reading your textbooks effectively and efficiently." It's not bad at all. There are several word documents you can download that may help you get past some of the common myths about reading.
Poking around on the Dartmouth site, I also noticed a video that contains most of the same information as the handouts, so if you don't want more reading about reading, there's an alternative.
This general advice is a good start, but it won't necessarily be enough to really master an extremely difficult text like Let Us Now Praise Famous Men. It will, however, help you master textbooks (like the Writer's Companion) really quickly.