How to get into oxford?Watch
The following are helpful:
Good GCSE results, depending on how competitive the course it (the standard for GCSE for medicine at Oxford is crazily high)
Good performance in admissions tests
Good performance in the interview
Good personal statement
you get the idea...
That said, it's quite rare for an application to be outstanding on every front. I remember the head of admissions at Churchill College in Cambridge saying that only about 2% of applications were that consistently good.
You will have to have the minimum levels required for the course you want to do. (e.g computer science - A*AA with at least A in maths/computer science at a level)
There is also your university application, you need a strong personal statement, experience in your field (but it is not necessary), you need to do many 'superparticular' activities related to your course (e.g attending Duke of Edinburgh, HE+, helping out with school open days. But your school will help you and tell you your options if you wanna apply there). You need to show you are genuinely interested in your subjects and uni course.
Then there is the interview. I don't know much about it as I didn't apply. But my friend who got an offer had a few maths questions asked, he was asked to talk about his book that he read and wrote about in his personal statement. (This shows you shouldn't write fake things as they can ask you in the interview.)