Reading math books to learn math does, at least at times, feel a bit like reading a dictionary to learn a language. Linguists and polyglots will affirm that this is a bad strategy. Instead, they will recommend that you go find some people who speak the language you want, and just start talking to them! If you run into something you don't know how to say, you can ask them how to say it, or refer back to your dictionary at that point.
That's how I learn math, too. I find some topic or problem that I'm interested in, then come up with my own questions to explore, and learn related information on an as-needed basis. That way all the new information is motivated by whatever it is that I'm trying to do, and nothing ever feels without context. I call it the "Carrot on a Stick" strategy.
Then, I just keep going with it. I'll tell to my friends about my carrot, discuss it with professors at my university, sometimes I'll even send emails to bigshots in the field asking what they think. (They usually write back!) I'm also big on running computational experiments, usually with something high level like Mathematica or GAP, so that I can just play and see what happens. Meanwhile, I keep writing and compiling my notes, and build up a document that contains everything I learned. When I get stuck, I can show this document to other people, or at least use it to convince myself that I've actually been working on something worthwhile. Occasionally, for smaller topics, this becomes one of my questions on Math StackExchange.
It's not the most organized way of learning, but for me, it's a lot more effective than reading books cold. My theory is that some people just learn better in "output mode." If I want to understand something, I can't just soak in other people's ideas- I need to produce. I have to write about it, make a simulation, or teach it to somebody else. So, whenever I start up a new subject, I look for a carrot to chase.