When writing my personal statement, how do I show my interest in the subject I am applying for?

This is vital. Just by stating you are interested in a subject does not prove to the admission officers that you are keen to study the subject. Instead you need to give evidence that you have gone out of your way to research or read around the subject, as only this really conveys that you are interested in the subject because you have some prior knowledge about the subject. One way of doing this is by writing a small paragraph on a specific topic area in the subject, expressing your opinion.