Spend time on the mechanics (understanding and writing out full proofs) and spend some time on the intuition (why is this important, examples and counter-exampl

Spend time on the mechanics (understanding and writing out full proofs) and spend some time on the intuition (why is this important, examples and counter-examples). If you keep doing this, you'll build up a whole library of examples and counter-examples for various statements and you'll get a feeling of how you can approach any problem (of similar difficulty). Start with any Real analysis I and Algebra I book, and try to understand every part of it - don't skim chapters, just work at your own pace. Your pace will improve over time, that's guaranteed. And keep doing the same thing - work out the proofs, exercises, examples and counter-examples. Re-read old ones, etc. A lot of math knowledge is really perfect or near-perfect understanding of the basic principles.