How do you utilize other people's words or work without breaking the law? The doctrine of fair use tries to provide guidelines. And it all comes down to how (and, in some cases, how much of) the material is being used. Fair use allows copyrighted material to be used for purposes such as reviews, research and teaching IF such use does not affect the potential market for, or value of, the copyrighted work. That is, are you impacting the creator's ability to profit from their work?
Here's an example: You need to create a spreadsheet for class. You work on it at the computer lab but want to work on it at home, too. So you--and this is an unlikely scenario!--manage to copy the software from a University computer and you install it on your home machine. You think that should be allowable, since the University is a non-profit and you're just doing something for class, not selling the spreadsheet you create. Alas, this would be a violation since by copying the software and installing it on another machine, you have affected the potential market for the software. That's not even close to fair use.
Similarly, if there was a great new profile of a movie star, full of shocking new revelations about their life, in the latest Vanity Fair and you decided to reprint all/most (or even the juiciest bits) of it in your (nonprofit) show biz blog, just credited the author wouldn't be enough, since you are keeping the magazine from making a sale.
Still, fair use is confusing. And even the Copyright Office admits that "the distinction between fair use and infringement may be unclear and not easily defined. There is no specific number of words, lines, or notes that may safely be taken without permission. Acknowledging the source of the copyrighted material does not substitute for obtaining permission."
Explore some the sites to the left for more detailed information. And for a cheeky discussion of the frustrating nature of fair use. Take a look at the below video.
Professor Eric Faden of Bucknell University uses snippets from a wide array of Disney animated works to illustrate copyright and fair use. Since Disney protects its works jealously, this video (which essentially attacks the abusive restrictions of copyright) parodies and attacks the very law it seeks to explain.