It came to me rather natually, actually. I like to read and write, in Chinese, initially. When I first came to the US, I tried to read some English books, but I couldn't finish the first five pages. I had to look up so many words from the dictionary that it wasn't fun any more. But I didn't have any pressure, so I basically dropped it. Two years later I picked up some books again, (starting from Agatha Christie's novels, one of my favorite readings) and I decided not to bother taking out the dictionary and just read. And that has done the trick for me. Later I read more things on different subjects. Another thing that might have helped is that I started reading online a lot the recent two years. Online news, forums, etc. This made me more comfortable with the CAT style of GMAT, I think.
For you, I think reading WallStreet Journal is definitely a good thing. However, GMAT reading materials cover a much broader range. The hardest ones are in the areas of law and medicine, for me at least. The trick there for me is not to care about details, and just try to understand what is the entire paragraph about. So if I was asked about a passage after I read it once, I would tell you something like this: "There was this case about American Indian's right for water. There had been some provisions about water rights for them in the law, but this case expanded their rights in certain specific circumstances, etc." I wouldn't remember the name of the case, nor the time of the case. I don't know if this is what they called skimming. But I can say that only reading the starting sentence and concluding sentence is NOT going to work for a lot of passages. Skimming for me, doesn't mean not reading some parts. It's just to focus on getting the main idea without paying too much attention to the details.
Regarding reading materials for you, remember what I said is to read as many passages as possible, but to limit the range of the materials to GMAT type readings. Also since there are only this many OG passages, you don't want to waste them for your initial practise. Re-reading something is definitely going to feel differently from reading it fresh. You need to use them at the most crucial time and use them for the maximum impact.