You must submit your UCAS application by 15th October using the UCAS Apply web link. The process from a Cambridge perspective can be found here. Note that you cannot apply for both Cambridge and Oxford.
As part of your application you will submit a personal statement. Follow this link for UCAS advice on writing a personal statement. This is about you and will be the same for all your applications. It is impossible to generalise on how different universities, colleges or even individual Admissions personnel view personal statements but guidelines from Cambridge are clear to the extent that the emphasis must be very much on your interest in your subject. Wider interests and achievements will only be seen as relevant insomuch as they might relate to your chosen subject.
The University offers a guide on How to write a great personal statement.
You are strongly recommended to identify any circumstances that might have adversely affected your education including disability, illness, long absences or other disruptions. You can inform the University with an Extenuating Circumstances Form, normally completed and submitted by the applicant’s school/college. The University is committed to widening access and particular attention will be given to this information.
A reference is expected to give an independent view of your abilities and potential. If you have difficulty in obtaining this, contact your chosen College for further advice.