Fair use is a legal doctrine that promotes freedom of expression by permitting the unlicensed use of copyright-protected works in certain circumstances without permission from the author or owner. Section 107 of the Copyright Act provides the statutory framework for determining whether something is a fair use and identifies certain types of uses—such as criticism, comment, news reporting, teaching, scholarship, and research—as examples of activities that may qualify as fair use.
To determine whether a specific use under one of these categories is "fair," courts are required to consider the following factors:
Remember that without the fair use doctrine, all copying of any amount for any purpose would be a violation of copyright. It is not the only exception to the exclusive rights of copyright, but it is the most significant. And it is of critical importance in the work of teaching and learning, and creating new knowledge.
Fair use is also intentionally -- and often frustratingly -- vague. It does not contain quantitative limits or absolutes, but rather a sliding scale of four considerations. It is up to the user to consider these four factors and decide if they believe the use they are contemplating is a legitimate one. In many ways, it would be significantly easier if there were a definite measure, but the law's non-specificity also allows for discretion depending on how you are using the material. No one factor is deciding and this is a good thing overall!
Remember also that you can always ask the copyright holder for permission to use their work. If you have their permission, you do not need to worry about making a Fair Use assessment.
Additional resources: Measuring Fair Use: The Four Factors (Stanford University)