I read and solved most of the problems from Walter Rudin's Real and Complex Analysis, Stephen Willard's General Topology, and a small collection of other books I bought with my limited funds and had shipped to me. I mostly bought from Dover, which has a very nice collection of quality math texts for very low prices, I will say.
My learning method was to try to get up to three texts on the same subject, so I could compare different treatments of the material. This was beneficial because if one text was unclear, I could compare with how the other texts explained this concept and it would hopefully dawn upon me what is right and makes sense. Other than that, I can say that I was at it 8 to 10 hours a day and in many respects, it was my one form of entertainment. I solved PDE's or proved theorems like other people did sudoku or crosswords. I looked at the problems as puzzles and tried very hard to solve them because it was all I had that was amusing. I also became very aware of how beautiful mathematics is and I truly began to love it. That passion helped a lot.