If your use doesn't fall under one of the exceptions to an author's exclusive rights, and if the work you want to use isn't in the public domain or available under a license that permits the use you want to make, you'll have to request permission from the author or copyright holder.
First, you have to identify the copyright holder. Next, you should request permission in writing, specifying what it is you want to use and how you want to use it. You should also make sure that you get the permission of the copyright holder in writing so that it constitutes a legitimate license. If permission is granted, be sure to appropriately attribute the work. If you don't get permission, or if that permission comes at too high of a cost, you may have to change your proposed use or use another work.
For more detail on requesting permission, see the Copyright Office's guide to making permissions requests.
Additional resources for locating copyright holders and obtaining permission, these pages written from the perspective of the United Kingdom but nevertheless are useful for the tips.