How do I convey my desire to study Medicine?

The key in Medical School applications is to 'show not tell'. An application is much stronger if a student has lots of evidence and examples of their enthusiasm towards the subject, rather than cliche phrases about 'passion' and 'childhood dreams'.

Having a range of work experience/ volunteering is a useful way to show interviewers that you understand the realities of a career in medicine (there are many downsides, and being aware of them is prehaps even more imporant than the positives!), and after serious consideration still have a genuine interest in persuing a career in medicine. Keep a notebook during your work experience, and for each day note down: what you enjoyed; what you learnt; what surprised you; reflections on your own actions/ personal skills/ communication skills; how you could further explore the disease/ patient management/ background science. 

By doing this, you will have a huge amount of well-thought out examples which you can use in your personal statement and interview to illustrate any points you wish to make. Furthermore, if you can link these examples to current news stories, ethical dilemmas, or extra-curricular reading it will show a genuine and comprehensive interest in the field.