Copyright Basics (Princeton University)
Copyright guides from other universities:
Code of Best Practices in Fair Use for Academic and Research Libraries: http://www.arl.org/storage/documents/publications/code-of-best-practices-fair-use.pdf (Association of Research Libraries)
Code of Best Practices in Fair Use for the Visual Arts: http://www.collegeart.org/fair-use/ (College Art Association)
Intellectual Property Rights (IPR) and Copyright: http://vraweb.org/resources/ipr-and-copyright/ (Visual Resources Association)
Selected copyright calculators:
http://commons.wikimedia.org/wiki/Commons:Hirtle_chart (general public domain chart)
https://pro.europeana.eu/resources/standardization-tools/public-domain-calculator (Europe Public Domain materials)
Digital Images Rights Computator (Visual Resources Association)
If you've determined that the image you want to use is likely protected by copyright, your next step is to identify the rights holder and ask for permission to use the image. http://copyright.princeton.edu/obtaining-permission has some suggestions on where to start.
ProQuest's Copyright Guide (for grad students submitting their dissertations) includes a sample permission letter.
Your publisher will specify the image format and resolution they require. Often it is best to pay for a publication-quality image supplied by the rights holder or taken by a professional photographer.
Submitting Your Dissertation or Thesis to ProQuest links to two brief and useful guides: