Also after you've done the homework, make sure you consult with your teacher about things that troubled you. Having battled your way through so many examples, you will be able to appreciate their explanation better than if you never tried them.

Good luck!

  Having no background in even basic high school math has killed me, failing pre-calculus twice now.

For anecdotes: I took the calculus sequence at a community college, and the teachers I had for (differential) Calculus I and (integral) Calculus II were among the best teachers I had at any level. The Calculus I teacher, the late Jack Minnick, was the best teacher I had in any discipline and at any level. He also published some math texts.

The key takeaway from both those instructors is that both had quizzes based on the homework material essentially every class, a methodology that pre-empted my tendency toward procrastination.

YMMV

After failing calculus once, I decided to go into physics (because, really I am an idiot), but I knew I needed to up my math game. I camped out in the library and saw a whole bunch of foreign students memorising stuff. Now, I used to scoff at this kind of behaviour, but I thought "I just failed calculus and now I want to go into physics", so what the heck -- nothing is crazier than that.

I sat down with a deck of index cards and I wrote a memorable name on one side and a theorem, lemma, equation, proof, etc on the back. I think I wrote something like 600 of them for my calculus class. And I memorised them -- all at once (because I'm an idiot).

But something wonderful happened after I memorised the cards. When I started to do example questions... I understood them... completely. The answers were blatantly obvious. All I had to do was write them down.

Well, very unfortunately, Physics was super hard (who'd have thunk it) and I still wasn't that great at math, so I switched to Computer Science. I was so intrigued by math, though, that I enrolled in every course I could fit in. Bizarrely, due to a miscalculation on my part, I accidentally graduated with a math degree and had to go back to convert it to a CS degree (like, I said, idiot).

Anyway, the point is that you can't speak without vocabulary. And even if you understand the vocabulary, you can't use it if you don't intuitively have a feeling for where it is appropriate. I later became a teacher of English as a Foreign Language and learned that language acquisition comes from repeated exposure to things that you comprehend.

If you memorise things, you won't acquire it, but it gives you a kind of super fast dictionary in your head that you can use to build comprehension. Then if you repeatedly expose yourself to natural language (problems in your text book, and especially proofs) you will acquire the language. After a while, it will just come naturally to you. However, the key is first memorising (see note) and then repeatedly exposing yourself to it over time.

Note - memorisation is not strictly necessary, but it saves a huge amount of time because either you have to keep looking things up that you don't understand (which is very tiring), or you have to expose yourself a billion times so that you understand it from context.

I highly recommend using spaced repetition software (Anki is great and perfect for this as it can handle LaTeX input) and work through your text book adding everything that could possibly fit on a card. Get creative about ways of breaking things down that don't fit on a card. Go through about 20 every day and review every single day. Do a couple of problems in your text book every day. At one point it will just "click" and everything will be obvious. It's kind of magical, really. I'm not saying you will be a math genius, but every casual undergraduate math course is doable by the average student, IMHO. Good Luck (even though you won't need it!)