Studying Natural Sciences at Cambridge was among the best things I have ever done and I highly recommend applying. The quality of teaching was generally excellent and I learned from some truly incredible people (including/especially other undergrads!).
Natural Sciences at Cambridge is a three-year undergraduate degree (with some fourth-year integrated masters options). It works differently from other universities in that you cannot apply for a straight Biology degree for example—everyone enters the same course and picks the modules relevant to them. By third year you specialise in one subject e.g. Zoology, Chemistry, Materials Science etc.
For example, I studied Earth Sciences alongside Biology in my first year and by third year I had specialised in Zoology (which is really more general ecology and evolutionary biology).
One of the best things about the course (and Cambridge in general) is the supervision system of teaching where you participate in small groups of one to five students and discuss lecture content with a supervisor (an academic of some kind, anything from research masters student to former head of department). The supervisor sets homework (essays, problem sheets) of a similar format to the exams. These discussions are where a lot of the real learning takes place.
Here are some free online resources that you might find useful when preparing an application.
Natural Sciences reading list - these are books endorsed by the people running the course. This list is probably the reason why so many people write about Why Chemical Reactions Happen in their personal statement... I would suggest picking one of these books that particularly piques your interest rather than trying to read multiple.
MyHE+ - this is a resource designed by Cambridge to make you think about your subject beyond the A-level curriculum. These topics are the kinds of things that you might write about in your personal statement.
3blue1brown - excellent videos about ~undergrad topics in maths, fairly accessible. In first year of the degree itself I was very glad I had watched the first few videos of his linear algebra series as it really gave me a good intuition for the topic.
The scientific literature - I honestly think we just searched keywords we were interested in on Google Scholar (a search engine for papers) but a better method might be to read some articles on BotanyOne and similar magazine-style sites to hear about what kind of research people are excited about at the minute.
Application statistics - some people take the acceptance rate of a college into account when choosing which to apply to. Whether this actually improves your chances of getting in is another question.
STEM SMART is a tuition programme for students from disadvantaged backgrounds. It is part of Isaac Sciences which is open to everyone and has problem sets for the natural sciences.
Do not do what I did and mention a book you haven't finished reading in your personal statement—you will get asked questions that you can't answer!
The interview is probably the most important part of the application process. Note that most applicants seem to get an interview if they look like they will fulfil the entry requirements.
Interview questions generally follow a very specific and distinctive format. Each question discusses some topic that you may or may not have any prior knowledge on. The question is broken into multiple subquestions. Each subquestion will begin with a prompt that you have to respond to (e.g. “sketch this mathematical function”). When you get stuck the interviewer will help you along, so no subquestion relies on you getting any previous subquestion correct. Sometimes they will require a large leap in logic that most applicants are not expected to get; answering one or more of these correctly is generally a good sign.
The focus of the interview is not how much you know already. It is how you respond to new information. The interviewers want to know if you can process, learn, and use information you haven't seen before. They are thinking about if you can handle the intense learning of the course. To that end it is important to show your thinking: talking through your answer, giving multiple possibilities and explaining why each might be correct, showing your working through a mathematical problem etc. If you are not sure you should say what you think the answer could be rather than ‘I don't know’. Being wrong is not really an issue if your thinking is clear.