What are some good things to make explicit between a student and his supervisor when beginning a PhD?
Having a discussion about the PhD project specifically and expectations in general is always a good idea. If there is a clear project lined up it will be useful to discuss the details, possible directions, publications etc. In some cases (systems/programs/traditions) it is useful (in fact mandatory) to write a research plan or to write a review of the field as part of reading up on it. It is necessary that both you and the advisor has the same view of what should be achieved to the extent the specific program allows.

Apart from the science it is useful to discuss expectations so that you can agree on how work should proceed. Should you meet regularly? if so how often? How much feedback should you expect? Well the questions are many but having such a discussion is useful, particularly if you can also note what you agree upon on a piece of paper. In my country, one actually signs an individual study plan that is followed up annually showing progress in terms of course work and research. having such a plan is actually constructive in that it makes it possible to see if you are on track and also identify if and when your plan needs revisions and goals may deviate from the originally proposed. But, of course, all this is something which to some extent is dictated by the traditions in the specific program.

So do take the opportunity to have a good talk about the future collaboration. you will robably sense if the discussion is received well by the advisor and adapt accordingly.