How do I write an Oxbridge personal statement?

For this I would advise three key points.

(1) Remember you're applying to study a subject not, for a career. At Oxbridge there is a special emphasis on this and the people responsbile for admissions will be looking to see your passion for the subject you are going to study, not the career you want to use the degree for. Therefore, work experience can be good but what I'd advise as being even more useful is attending masterclasses or taster days where you can experience studying the subject and comment on that. Further, you should have at least three, substantiated and different reasons for why you want to study the subject. This should form the longest part of your statement. 

(2) A common trap is to think that Oxbridge tutors are looking for a long list of impressive achievements in a personal statement. From my experience, selectively choosing a few achievements and going into detail about them will prove to be a much more successful approach. Primarily, you will get into Oxbridge for your mind and therefore it's better to go into depth about a few achievements so they can see evidence of you thinking. Mention what you learnt, analyse how that has been useful, give your opinion. 

(3) Approach an Oxbridge personal statement as an essay rather than a statement. You should be making a strong argument throughout (arguing and persuading for you to be given a place). There should be a sense of voice throughout, be critical (evaluative) about experiences or things you've read, develop your sentences, but keep it formal and true to yourself.