Although the concept of reasonable use of copyrighted material had existed in various guises before 1976, Fair Use was given the specific form it inhabits today as §107 of the U.S. Copyright Act. At the same time, the Copyright Act refrained from defining Fair Use in terms of specific allowable uses. Instead, the language of §107 leaves everything to interpretation based on the details of every individual instance. Indeed, the breadth of situations where Fair Use might apply is demonstrated most clearly in the very brevity of the statute itself. Comprised of an introductory paragraph and four "factors," solid definitions of Fair Use exist only within the case law that has dealt with it.
The complete statute
§ 107. Limitations on exclusive rights: Fair use
Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include —
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work.
The fact that a work is unpublished shall not itself bar a finding of fair use if such finding is made upon consideration of all the above factors.
That's it! From there, it's just a question of figuring out if the use is specifically a "fair" one or not. To do that, you need to look at the four factors individually and weigh them against each other.