Existing compilations of the information you need to be a PhD student at NSOE:

Your number 1 resource:

The NSOE Doctoral Handbook 

Broad handbooks and lists of resources that are currently maintained:

• Nicholas 411: “a one-stop home for all the resources you need as a member of the Nicholas Community.”  Topics include how to update your various Duke-related web profiles, requirements to drive a Duke vehicle, how to order business cards, and other practical information specific to NSOE.
• Nicholas School of the Environment Bulletin: handbook for all NSOE students.  It includes information useful for prospective PhD students, a summary of fellowships and assistantships, coursework options, and descriptions of the structure of the school and associated entities.
• Duke Graduate School Student Handbook: searchable web-based documentation of policies and resources that apply to all Duke graduate students.
• Graduate Student Resources: fairly comprehensive list of links to resources for all Duke graduate students (not NSOE-specific ones), including Duke Graduate School forms, the academic calendar, disability accommodation, recreational opportunities, international student needs, etc.
• Duke Student Affairs: You probably are familiar with Duke’s landing page for students, which links to many of the resources all Duke students use most often, but Duke Student Affairs also provides more detailed guides to issues like diversity and community involvement.
• Graduate and Professional Student Council (GPSC) Resources and Services: official student-curated list of resources for Duke Graduate students within the university and in Durham, including things to do, political contacts, and places to go when you have a problem.
• GPSC Student Survival Guide wiki: crowd-sourced list of information that Duke Graduate Students have found useful, including about free activities, places to eat, and childcare.

For specific PhD programs:

• Earth and Ocean Sciences (EOS): Program Requirements and timeline/procedures
• Environment (ENV) Info for Enrolled Students
• Marine Science and Conservation (MSC) Info for Enrolled Students
• Integrated Toxicology and Environmental Health (ITEHP or TOX) For Current Students
• University Program in Ecology (UPE) Current Students
• University Program in Environmental Policy (UPEP) student handbook and other info (see submenus)

Old, but still useful:

• NSOE Doctoral Handbook: pdf from the 2009-2010 school year.  As you would expect, this handbook is well out of date; please do not rely on it for official program requirements or anything similarly important.  However, much of it remains useful, and it can point you to resources which still exist.
• Nickipedia‘s “PhD’s: Helpful Info“: resources compilation by past NSOE PhD students, apparently made to complement the above doctoral handbook at around the same time.  This mostly abandoned crowd-edited site still has useful tidbits you won’t find elsewhere, like a library of past prelim proposals.