How do I demonstrate an interest in a subject in my personal statement?

Honestly, it depends on the subject that you are applying for. However, often a good way of demonstrating your interest is to relate it to past experiences or activities you have done. For example, if you were applying for maths, it would be a good idea to mention if you had taken part in any work experience in industry or had completed extracurricular activities such as the STEM project or EESW. Mentioning reading on the subject can also be a good idea, for example if you were applying for philosophy, it would be beneficial to mention reading someone like Kant or the like. However, you must be able to discuss any experiences you mention in your statement at potential interviews, do not say you have done these things or had these experiences if you have not, its best to be honest about who you are and why you want to do your subject.