Learning math is hard. Those that have braved some of its depths, what did you discover that allowed you to go deeper?
This is a place to share insights, methods, and tips for learning mathematics effectively, as well as resources that contain this information.
Advice on the basis of my personal experience:
Learn to pinpoint your confusion.
Train yourself to follow your confusion to its source. Often, doing this is most of the work of clearing it up.
Develop intuitions through simple, canonical examples.
While you need to be able to express concepts formally, these expressions should flow from your mathematical intuitions. You can build these by using simple, representative examples, and by connecting the new concepts to intuitions you already have.
Connect the definitions and theorems of an area into a conceptual map detailing how they relate to each other (Vladimir_M elaborated on this here).
Try to do this across mathematical areas as well, to get a coarse map of all of mathematics.
Work problems (either given by others or of your own creation).
It's tempting to think you understand the material by just reading. While you can avoid feeling stupid this way (as SarahC mentions), you won't get to test your understanding. Problems also help to build and sculpt your intuitions.