The first thing to do is to identify your potential supervisor (or should it be appropriate, two supervisors) and get in contact. The sooner you can do this the better. If you’ve a specific research question/topic in mind, run it past them. If you’ve only got an idea of a period/geographical area/category of data in mind, let them know. Between you, you should be able to work out whether Durham will be the right place for your research, and if so, a specific application.
The University’s online application procedure makes it clear what you need to include. If you will be applying for a grant award competition to fund your proposed research (as most applicants will) you should work on the two together.
The tighter the focus, the more specific the research questions and methodology, and the most clearly argued justification for why this research is important and why it will drive the field forward the better. Pitch it at informed non-specialists (it will be read by archaeologists, but not necessarily by those expert in your field). Avoid jargon except where absolutely necessary.
Background to the research
Set the context: what exactly do you want to do; what has been done on it before, what is lacking, and where does it fit in; consequently why it is important. Include in this a brief consideration of existing literature (but not a full review); are there any leading texts or works of particular influence? Are they still current, or are they limited in any way?
We don’t need to be told how great we are, but do outline exactly what it is about the department that will facilitate your particular research. It will probably be a potential supervisor; your intended research may well relate to theirs. If so, does it complement or extend it in some way? Or would you be bringing something new to one of our research groups? You can get an idea of these through the department’s web pages and through discussing research groups with your proposed supervisor.
Research degrees will typically have a small number of specifically phrased questions (say 1-5). They should be well defined and reachable, i.e. not speculative without any means of investigating them.
Methodology and materials
How will you investigate your research questions? You will have identified a particular material or set of materials (sites, landscapes, ceramics, lithics, burials, settlements &c). What existing methodologies exist for their archaeological study; what of these will you use, and why? Will you have a developmental element, e.g. extending a particular method for the first time, or developing a new one? How tried and tested is your methodology? Is there an element of risk (not always a bad thing, but something to discuss with a potential supervisor). What about access to materials (other countries, museums, private collections &c); will this be an issue? A brief quantification/qualification of intended materials will help.
We cannot emphasise enough that research degrees must be completed in a particular time period. When you commence a research degree with us your supervisor/s will help you plan a working timetable, and the department conducts reviews to help you with progress. But a rough idea from the outset of how your 2 or 3 years will look will help. Typically the first third or so of this period is spent preparing the research, i.e. with a full literature review and analysis, isolation of specific fieldwork requirements (what materials/sites &c will be seen) and methodological requirements, and a planning of the fieldwork stage (which might well include the lengthy bureaucracy required to gain access to sites and materials). The second third is taken up with doing the fieldwork, i.e. gathering your data and analysing it. The final third or so is spent considering the implications of your results and writing the project up as your thesis. Breaking your proposed timetable down into 6 month blocks is a good way of approaching the application; remember though, nothing is cast in stone and things do get modified.
Does the department or university have everything required for undertaking your research? This is something that will be clear, or which you can discuss with the potential supervisor.