If you have determined that your use is not covered by any exceptions (Classroom Use, Fair Use, TEACH) and that the work is not in the public domain, you will need to ask the copyright holder for permission.
See model permission letters from Columbia University, and sample letters from College of DuPage.
When asking for permission:
Be as detailed as possible about how you plan to use the work. Include things like the number of students in your class, how long you plan to use it, exactly what portions of the work you want to use, etc.
For journal articles and books from major publishers, rights are often handled by the Copyright Clearance Center. You can go there and search before sending a letter. Permissions in the CCC will virtually always be granted for a fee.
Know that in many cases you will be quoted a fee for using the work. You can attempt to negotiate this fee.
Be prepared for it to be a lengthy process. Just tracking down the owner can take a long time and response times can vary quite a bit.
Remember that the creator is often not the copyright holder.
Visit the Harper College Copyright & Fair Use page for more information.