In theory the process for using the work of others in your publication is straight forward:
1. Ask yourself if you need permission. Is the work in the public domain or distributed under a Creative Commons license that allows reuse? Proquest International (the company that publishes the Dissertations and Masters Theses database and the system widely utilized for registering dissertations and theses) has produced a useful guide for determining when you need seek permission.
2. Determine who holds the copyright to the material.
3. How do you want to use the copyrighted material and what rights will you need.
4. Contact the owner to negotiate permission and whether payment is required.
5. Make sure that your permission agreement is in writing and that you retain it.
These steps are explained in depth in The Basics of Getting Permission guide from Stanford University Library.
More 'Getting Permissions" guides
The Columbia University Copyright Advisory Office has an excellent web site covering most aspects of copyright; it includes a very useful section on seeking permissions.
Obtaining Copyright Permissions
A guide from the University of Michigan Libraries offering strategies and resources for obtaining permissions for text, photos, fine art, music, film and works in other formats.