The first time I self learned a subject was really calculus. I taught myself calculus using an old advanced calculus book they used to use at MIT in the summer before senior year. I basically spent two weeks reading 24/7 of that during my summer break, and I learned to write proofs by noting careful details, in a notebook, of how they proved each and every theorem in that book. After I finished reading the book in those two weeks, I basically spent the next two to three weeks doing every single problem in the book, and the way I verified whether my proof was right or not, was by scrutinizing particularly hard problems for several hours, while working on other problems. I usually skipped the routine exercises, since they don't really teach you much except motivate memorization of techniques by repetition. But if you need to do these type of exercises, go for it! The types of problems you should focus on are the theoretical ones because these will immensely help you with understanding how certain ideas come about. And don't be discouraged if a certain idea might take you a couple hours to days to understand, its all part of the learning process. Try to figure out why the idea works by yourself, and then ask someone. Never ask someone for help unless you have spent at least a week thinking, and you still don't understand the idea.Also don't feel hesitant to teach yourself other subjects. After I finished the calculus book I taught myself Abstract Algebra, Graph Theory, Mathematical Logic, Set Theory, Number Theory, Statistics, Linear Algebra, Ordinary Differential Equations, Fourier Analysis and Differential Geometry. And all of this was done in one year. You'll be pleasantly surprised how quickly you can pick up learning a subject after teaching yourself something for the first time.