Uni in America, how does it work?

Say I wanted to get into Harvard, what would I do? What is the application process like e.g. In the UK of course, You need to do A levels and a personal statement then apply to UCAS and so you get 5 choices of different universities that will either Reject you or accept you dependent on your A levels. Also what A level grades would I need to get in Harward (e.g. say for computer science or something) ?

you would need way more than good grades to get into harvard.
Theres an entry exam, probably an essay to write as well as interview to get through.
If you want to go into harvard, you should have started preparing before GCSEs

So is getting into a top uni in USA harder than a top UK Uni e.g. Oxford?

Most american universities don't have a 'standard offer' when it comes to grades, it really depends on how good your overall application is. Conditional offers aren't really even a thing in the US, usually once you get an offer that's it, you're in unless you mess up your final exams really bad. Top schools may give a condition but it won't be a particularly difficult one to achieve compared to the offers top UK unis give out. I'm not too sure what sort of offers A-level students get exactly, as I already had my A-level results when I got my offer from Stanford, but I do know a friend of mine got into Princeton with just ABB, and she did have some sort of condition for entry. I think it was AB with an A in maths or something like that, so definitely not the toughest offer out there.

You're going to have to sit for the SAT, and most top schools will ask for 2 SAT subject tests as well. Harvard recently dropped the subject tests requirement, but unless you can't afford to sit for the tests you should take them. I'd advise you to read the application requirements on the website of every single university you intend on applying to, as admissions differ from university to university. Most top unis will accept (some even require) the Common Application or Universal College Application, both of which are similar to UCAS in the sense that they allow you to submit the same application for every uni you apply to. However, some may require you to fill out something extra (for example: Harvard states that you need to include 'Harvard College Questions for the Common Application or the Universal College Application Harvard supplement' in your application), so again, please check out the website of every university you apply to and read their application requirements.

As for how 'difficult' it is to get into top US unis as compared to Oxbridge etc, that depends on you really. It's just two very different application systems, it's a more 'holistic' system in the US where extracurriculars are a very big deal, whereas in the UK it's very focused on grades and academics. Even the interviews at Oxbridge involve mostly academic questions, whereas interviews for US unis are more general/'casual' (do note that, as far as I know, interviews at top US unis are not compulsory. If there are alumni near your area willing to be an interviewer, they may offer an interview that could help your application if you nail it, but if you're confident enough in your application you can decline without any negative impact on your chances). Some people can get A*A*A*A* but lack what schools like Harvard are looking for, whereas some people may not be able to get good enough grades to meet the requirements for unis like Oxford/Cambridge/Imperial/LSE etc but have successful applications to Ivy League schools thanks to having a more 'well-rounded' application.

Other things to think about-- as an international student, you may score some points for being exotic, and that could help your application.

On the other hand, there is a lot of financial aid you might not get as a result, and sticker price is not as low as in the UK.

It depends on the college. Harvard gives the same financial aid opportunities to international students as they do to american students, whereas some other colleges have limited financial aid for them. The smaller colleges you mentioned probably won't offer anything in terms of financial aid.