The GE requirements mean exactly what they say they mean. There are university requirements, which everyone (regardless of college) have to complete. For Muir’s GE requirements, you have to take a social sciences sequence (3 courses), a math/natural science sequence (3 courses), and a sequence (3 courses) from two of the three areas: fine arts, foreign language, and humanities. You also have to take two writing courses (MCWP40 and 50). If you have AP credits, you can find what courses they count for here: http://www.ucsd.edu/catalog/pdf/APC-chart.pdf. The overlap rule means that only three of the classes you take for the major can overlap with GE requirements.
So for example, let’s say you’re a cognitive science major. You have to take Muir writing (MCWP 40 and 50) regardless of your major, so you pick those. You have to take calculus for your major, so let’s say you take MATH20A, B, and C (the first three calculus courses, which is a year’s worth of calculus). This can count as your math/natural science sequence for your GE requirements, while also fulfilling your major requirements. Now, you have to pick a social science sequence. It can be any one you want that is listed on the website, except the cognitive science sequence because you are already taking COGS 1 for your major (only three courses you take for your major can also count as GE requirements, and you already used that up when you used calculus to fulfill both math and cognitive science major requirements). So let’s say you pick anthropology instead, and take ANTH 1, 2, and 3 as your 3 course sequence. Now, you decide that you really hate foreign languages, so you’re going to pick a fine arts sequence and a humanities sequence. You pick music as your fine arts sequence and choose three classes from the list provided: MUS 4, 8, and 15. You took AP US History in high school and got a 5 on the AP exam, so you’re exempt from two of the three required courses for the US history GE sequence. Per the chart above, you can choose HILD 2A, 2B, or 2C to complete this requirement, and you choose HILD 2B.
Now, of course, you don’t have to make all of these decisions up front, but that’s a sample plan of who you could finish Muir’s GE requirements. You can really pick whatever you want from the options, as long as you have one sequence from each required field. And of course, it’s not like you’ll take all of these courses in one quarter. They’ll be spread out throughout your first couple of years (or more if you choose to spread them out even further. The only requirement is that I think you have to take Muir Writing within your first two years.
At orientation, you’ll talk about GE requirements more, but it’s really not that difficult. An advisor will recommend courses for your first quarter at UCSD, but you don’t have to take those courses if you don’t want to. Your first quarter will likely be a couple of major prerequisite classes (like calculus or cognitive science and such) and a couple of GEs (like MCWP40 and your choice of GE). From there, you’ll figure it out.
You can double major in any college. You just have to fill out a double major petition and get it approved. As part of the process, you are going to have to put together a four or five-year plan with all of your major, GE, and university requirements, showing how you plan to complete all of the requirements. This is your responsibility. Go to the major’s pages and see what their requirements are, and make a plan with all of the requirements, showing when you plan to take each course. You don’t have to do this right now, and you can ask advisors in each department for help planning if you need it. However, I think computer science is impacted, so I don’t know how that works with regards to double majoring. You should ask an advisor in that department. It may be a competitive process to get into the computer science major.
This http://muir.ucsd.edu/academics/sampleplans.html might help you plan. You’ll also have a degree audit, which you will eventually be able to access through tritonlink. This will have all of your requirements for your major and college, as well as university requirements. They will list courses that you need to take in order to complete a requirement, and they will show which requirements you have completed and which ones you still need to complete. That will likely help you as well.