What's the best of way of going through a math textbook for self-learning (and not for a class)? I ideally want to read material and spend most of time on solving problems in the book. My struggly with reading books myself is that I tend to get bored in the first few chapters when the book introduces basic machinery that's not particularly interesting. How does one get through these parts of the book, and what are some things to keep in mind while self-studying a textbook?
Self-learning and book-reading are skills that should be practiced and developed properly. I can't imagine a single answer here getting the job done. If you want to dive into it there's a terrific book called "How to Read a Book: The Classic Guide to Intelligent Reading" (Amazon link for convenience) by Mortimer J. Adler.
It gives a great framework for book-reading and you can generalize it to any kind of self-learning, also, it deals mostly with expository books (Textbooks). It addresses your boredom issue as well.
Every learner should read this book. Especially self-learners.