I loved Cambridge but honestly the Computer Science course was pretty poor. It won't have helped that the best first-year lecturer, Arthur Norman, retired recently.
You're taught in faculties just like anywhere else. There is a Department of Computer Science or Department of History or whatever, and those are where everyone goes for lectures. You have 1-to-1 or 1-to-2 teaching sessions in your college (or at least, organized by your college), with some kind of relevant academic in the college (taught by a PhD student, PostDoc, professor, depending on who is availble, who the director of studies thinks is good, what level of undergrad etc).
The analogy usually used for the benefit of American-tourists (not meant patronisingly, it's just empirically surprisingly effective) is that it's like Hogwarts. You have the colleges/houses (like gryffindor and hufflepuff) where you live (at least in 1st year) and eat and play sports for, but lectures and the degree in general (like potions class) are all done in faculties with people doing the same course but in other colleges.
Most lecturers and professors will belong to a college too, but they'll still be lecturers in a faculty rather than a college. In Cambridge there is an academic rank called 'College Lecturer' but like most things that doesn't mean what it says, and is probably designed to confuse and intimidate foreign people, like everything else (for example May Week when all the college balls are held after exams, is in June, and the weeks start on Thursday and end on Wednesday). [Lest the po-faced take me seriously, it's not actually designed to confuse people, it's just there's a lot of vestigial baggage that it's not worth the effort of changing [like removing an appaendix when it's not causing you problems] when you've been around almost a millennium and where a switch to the Gregorian Calendar was more recent than when the desk in your study was built.]
Lectures are organized by the relevant subject's department, independently of the colleges; in many ways the departments are as autonomous as the colleges. But supervisions, the more important part of the Cambridge style of teaching, are organized by your college (though smaller colleges with only a few students in a given subject will often share supervisions, and even the biggest colleges might send you elsewhere to be supervised if you've picked an obscure specialization in your third year). Almost all colleges offer almost all subjects (there are a few special cases like st edmund's which is a dedicated theological college AIUI), but some do have a reputation for particular subjects; many (but by no means all) computer science students (in general most students don't have a minor in the UK, especially in Cambridge) go to either Trinity Hall (for its history/reputation and its generous internet usage policies) or to Churchill (which is physically closest to the Computer Science department)
In my college there were four computer scientists in my year. We had two lecturers in the college, who gave us tutorials. Then we join the rest of the computer scientists throughout the University for lectures.
And the colleges are more than semi-automonus - they have their own academics, own money, and they do their own admissions.
I'm judging from the first-year course, which I was so unhappy with that I switched to mathematics; maybe it gets better later on. But what I saw was an operating systems course that was basically rote memorization, and two programming courses that taught very little; the ML course spent too long teaching the very basics, and students were handheld through the only actually contentful exercise. The java course was supposed to be more about real-world programming, but taught very old-style C-in-java that would be undesirable at any company I've worked at. It was all just very boring and useless; my supervisor tried to introduce some more interesting exercises (my supervision partner found it all equally trivial), but by the end of the first term he'd given up on finding us anything challenging. Conversely at least two of my friends passed all the exercises and the exams but quite clearly had no understanding of computer science or how to program.
