I am currently serving on our Promotion & Tenure Committee. We have been fortunate in the department to make some terrific hires in the last few years, and the different ways that these newbies represent themselves in their P&T documents surprised me. So, first, these questions all share a subtext: Who do you want to be as a professional?
Once you have found your feet (which usually takes the first year), you need to focus on the next 4-5 as one long continuum. You and your work will be intimately connected for the long run toward tenure, so you'd best love what you choose in order to maintain your intellectual energy and excitement--the qualities that make good work possible. If the "what" exists in the same general area as your diss, that's great. But if not, if the diss has paled, this is the time to refocus. Success demands serious reflection on this topic; you need to clearly understand strengths and weaknesses, both yours and your institution's. Your research focus should, ideally, be closely connected to your teaching interests--one informs, shapes, alters the other. Your research also needs to be practically manageable and capable of producing multiple publications and conference presentations over the course of the next few years, including The Book (most important if you are at a Carnegie 1/Research Extensive University, but always desirable).
Once you know what you are interested in, you need to articulate clearly your vision of your immediate (2-4 years) future in terms of research, writing, and teaching. How to do that? As a recent grad student, you are familiar with theoretical and research literature in the field; look closely at those articles, books that delineate the authors' plans. Do they look like yours? Adapted, will they?
I think the trick lies in the ability to effectively envision both the big picture and the day-to-day details, kind of the way we approach creating a syllabus. What steps/stages can be identified as necessary to completing the desired goals? What sequence of assignments can you imagine and how will you implement them? How are these steps related? And how will you measure/evaluate your success?
Finally, how do you publicize your ethos/role in the department? This is tricky because you don't necessarily want to be perceived as a show-offy, know-it-all, BUT if you don't toot your own horn, as it were, no one will. Talk about your work with other faculty, offer to share progress/steps/findings etc. in informal faculty/grad student discussions or more formal presentations. If your department doesn't have a regular habit of faculty sharing their work internally, inaugurate one. These are terrific ways to connect with others and invigorate your (and their) intellectual energies, and playing well with others while you are demonstrating your seriousness as a scholar is a terrific way to establish your ethos--and better the general departmental climate.