The several comments suggesting mathematics and logic from scratch are spot on. This can be a bit overwhelming and dispiriting though. An alternative (or really a supplement) to an elementary proofs text is Raymond Smullyan's books of logic puzzles. Smullyan strikes the right balance between fun and substance.
The second idea is to try taking notes. Grab the latest copy of your favorite magazine (mine is Foreign Affairs) and write about the articles as you read them. What did the article say? How does it relate to the prior articles? Common topic? Contrary opinions? How does it relate to other things you've read in the past?
Asking these questions as you read can help to foster an internal dialogue and help you remember what you read and give direction on what to read next.
It's how I advise students who are reading academic papers for the first time and get overwhelmed by diving into the deep end of some subfield.