Contacting a potential supervisor
Your chances of a successful application will be greatly increased if you do some research to determine who would be a good supervisor for the topics you are interested in, and contact that person to discuss your interests and suitability for the degree programme.
How to make contact
Be targetted and specific
Some supervisors may not respond to an email from potential students that appears generic or unrelated to that supervisor's particular field of study. You should have looked closely at the person's web-page, even read some of their published work, and should introduce yourself by explaining why this person's work interests you sufficiently to apply to study with them for several years.
Include in the main text of your message (not just in attachments) a short statement about your background (what you have studied so far, your degree result or grade average, any relevant experience) and research interests. Also mention relevant information such as your funding situation. It is okay to attach a CV, but the supervisor may not read it unless you have already explained in your email why they should be interested in you as a potential student.
Academics tend to be very busy and it may take time for them to answer your email. If you get no reply after a week or two, send a follow-up email. If a first message followed by a reminder doesn't work, then you should start looking for an alternative person to approach. It may be that this supervisor is not currently taking on students.
If you are genuinely uncertain who to contact, then you can send an enquiry to the Institute or to the School graduate office, however you should read through all the available information about topics, institutes and supervisors first to narrow down your choice.
Note, it is also possible to change topic and/or supervisor once you arrive if your interests develop and change over your initial months of study.
Finally, it is possible to apply without having contacted a supervisor, but as already mentioned, you will improve your chances of success if you already have a confirmation from the supervisor that they are interested in your application. But be aware that final decisions can only be made on the basis of your formal application.