Choose a topic: begin with an idea of the area you wish to do research in.
Define your proposal: Do some research to refine this into a proposal complete with information concerning which sources you will consult and any training that you might require.
Find a supervisor: Search for academics working in the field you wish to study. There need not be an exact correlation between your proposal and their research interests, after all it should be a 'unique' project, but they should be equiped to advise you on secondary reading and where to find sources if relevant.
Contact your supervisor: It is best to contact your proposed supervisor before you apply. You can then discuss your proposal with them, ensuring that they are happy with the topic. They will also at this time be able to give you advise on your Research Proposal - particularly important if you are hoping to apply for funding.
Apply: Once you have been in touch with the supervisor and they have, provisionally agreed to your proposal, apply to the college for a place.
Note of advice: A research programme is entirely different from undergraduate study, and also from Master’s programmes in that students are expected to work for the most part on their own. When students decide on a general field of study, they should start to think about possible research topics within that field and after exploring the relevant secondary material should have fairly precise suggestions to make. Students should not expect a supervisor to devise research subjects for them, although supervisors will naturally help them to clarify their ideas. A vague desire to go more deeply into a subject, or to remain in a university environment, is an inadequate reason for embarking on a doctoral programme. Research should not be undertaken lightly; the preparation of a thesis is a long, arduous and lonely task, and only those with considerable stamina and a capacity for patience and perseverance are likely to stay the programme.