Tips for self-study with just a textbook and google
Your general plan seems good: Do a lot of exercises. An old proverb (Chinese, but maybe more general) is that you don't know something until you've practiced it ten thousand times. (Rule of 10,000). 

I've found wikipedia to be quite good, but not perfect, for questions on mathematics. Be a little skeptical if anything seems a bit strange in an article there. I once came upon an article that seemed sketchy in part - just a paragraph or two in the middle of a long piece. I came back in an hour or two and it was gone. A professional isn't likely to be misled, but a student should be just a bit cautious. 

Also, take notes. What are the most important three ideas in this section/chapter? Don't try to re-write the book, just abstract the gems. Highlighting has less impact since your brain is less engaged. You want to do things while self studying that are "active" enough that your neurons get rearranged. This is why the exercises are especially good.