People with severe RC issues usually need longer to get better than people with severe problems in other areas. It's tough to give an amount of time because it does vary so much from person to person, but it will take at least a month of regular study and possibly several to get a lot better if you have severe RC issues.
To start, you should get better at comprehension in general - outside of the GMAT. Here are some good sources for "GMAT-like" reading, courtesy of my fellow instructor Jad:
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http://magazine.uchicago.edu/ - particularly articles in the "Investigations" tab
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http://harvardmagazine.com/
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http://sciam.com/ (This can get a bit too casual for the GMAT, but it's worth including because so people get freaked out by science passages on the GMAT.)
Start by reading a paragraph and then writing down a one-sentence summary of that paragraph's main idea - NOT all of the detail, just the main idea. Write a full sentence first and then go back and think about how you'd write that information down in extreme shorthand during the test - what can you abbreviate or drop entirely? (Remember that, on the test, you only have to remember the information for 6-8 minutes and then you can forget about it forever, so you don't need to write things out as thoroughly as you normally would for notes taken during a class.)
After you get good at that, move on to writing a table of contents for an entire article, paragraph by paragraph. Again, table of contents = big ideas, not all the little details.
At that point, bring GMAT study back into this and start doing the above exercises with some GMAT passages. You may want to order some of the old paper-and-pencil tests and use those problems as drills, so that you can get better before you start to use the more recent material (OG, GMATPrep). Also, at that point, you need to identify what outside prep materials you're going to use. You don't mention whether you've already got materials from a specific company. You can use the time you're doing the non-GMAT exercises to identify which materials you want to use (aside from OG), or even whether you want to take a class or meet with a private tutor.
Then, just follow the study method of whatever materials / class / tutor you decide to use!