Answer by Richard Muller:
I had a graduate student who, as an undergrad at Cornell, had more A+ grades than As — about 15. Once I asked him how he did that. "I use tricks" he said. They all seemed so obvious when he told me, that I'm not sure I can recall all of them. Below I'll mix in what he said with some of the things I observed in other great students.
He said he always read the assignment before lecture, not after. Do that, and you know what to pay most attention to. You can ask questions about things you didn't understand. You can't ask a book questions, but you can ask a professor. Moreover, your professor will be impressed that you ask the best questions. Remarkably, it takes no longer to read all the material before class than after class.
Visit the professor during office hours. Some professors will just try to intimidate you into not coming so often; ignore them. Some will be delighted to have visitors. It is a great opportunity to interact with a very smart and very knowledgeable person.
Don't try to learn what you think is important, but try to learn what you think the professor thinks is most important. That's really why the professors are there; they have enormously more experience in the subject, and know what is really important. You'll discover you do much better on exams.
Find other students to study with. College is not a place to try to prove you are better than everyone else; it is a place where, among other things, you can learn how to work well with other people. Try throwing good questions at your friends. It turns out that thinking of good questions gets you very far. Don't be surprised if some of the questions turn out to be the same ones the professor asks.
Go to lecture and, particularly if it is boring, try to figure out why the material is actually fascinating. All those courses are there because someone thinks it is important, even if your current professor doesn't. Once you become interested in the material, it will be easy to learn; in fact, it will be hard to forget.
Recognize that not all the material is equally important. See if you can identify that. Think hard about the important stuff.
Take this to be your top homework design: there is a person who has limited time, not really enough, to learn some material. What is the best way to approach that? Pretend that that question is a homework exercise, and write a page. Then follow your own suggestions.