This is very much what I did, but I would add two other things: study above your level, and read the history of the subject.
If an undergraduate read graduate level textbooks, especially overviews.
This gives one a sense of the context of the subject, an appreciation of "where it's going", a hint of why the subject is still interesting and under active development, and makes the undergraduate material seem almost innocent by comparison. It's much harder, of course, and you'll often find that the entire semester's material is covered in a couple of chapters at the beginning, but the feeling of "how the professionals really talk/think about the subject" is hugely important for getting a feel of the thing.
The history of a subject is great for giving the human context, which is hugely useful for grokking how things developed organically, as well as the personalities involved. It can really help remembering stuff.
Before going back to college to do Maths and Physics I went out to the local university to get advice as to how to study the subjects. I was told to get Feynman's Lectures ((in)famous) and Boas' Mathematical Methods in the Physical Sciences (extremely terse but excellent). I did, tried my best, and in retrospect still think they were taking the piss. And yet, when I went back to university a year later, there were so many ideas and intuitions already in place that although the Maths was still computationally difficult the concepts were not as strange as they might have otherwise been.
In college itself it was the library that was the real draw, so many amazing texts just there for the reading. To be fair, the professors were wonderfully patient and encouraging.
But mainly, just keep at it, hour after hour, without comparing yourself or your efforts to anyone else. It's hard enough without imagining other people looking over your shoulder. I remember a number of young ones who, though brilliant in school, found university just that bit beyond them. Take frequent breaks, even holidays, and remember, above all, that exams are perhaps the worst test of learning we have yet devised apart from all the others.