Under the “Fair Use” rule of copyright law, an author may make limited use of another author’s work without asking permission in some situations. An article on the Nolo.com site provides a good review of the Fair Use rules. For more information and the five rules to keep in mind about what is Fair Use, see When Copying Is Okay: The “Fair Use” Rule.
Tips on Getting Permission to Publish Material on the Web
Nolo.com has a good article about how copyright applies to what you put on the Internet or an intranet. For 10 tips about how to get permission to post copyrighted material, see Getting Permission to Publish: Ten Tips for Website Managers. The first tip is to assume anything you want to post is copyrighted and you can’t post it without the owner’s permission.
The last page of the article provides some links to collectives and clearinghouses that organize and license works for their members. For example, if you want to reprint a New Yorker cartoon, go to https://cartoonbank.com.