I got into Berkeley this year for Engineering, so I can help you a bit if you need.
First thing you need to decide is whether you want to apply for computer science through the college of Letters & Science or the College of Engineering. The latter is considerably harder to get into, and the course will also be more rigorous and "prestigious" (if that matters at all to you).
I provided my GCSE results in the "additional information" section of the application, as well as my predicted IB score (equivalent of A levels, if you haven't heard of it). The entire application is done online, which makes things MUCH easier. You need to self-report your transcript grades from Year 10 onwards (they will only need proof of these grades if you're accepted), and there are no teacher recommendations required. If you're a borderline candidate, then you might be sent a supplementary application to fill in around January or February, which may require teacher recs, more report grades and stuff like that. If you don't get one of these, I believe it's safe to assume they've already made their decision about you.
The great thing about the application is that if you're interested in applying to other UCs like UCLA then all you have to do is add it from a dropdown.