Some common assumptions are wrong
Many people assume that everything posted on the internet is public domain, probably because our law used to protect published works only if they displayed the proper copyright notice upon publication. The law, however, has changed: neither publication nor a notice of any kind is required to protect works today. Simply putting the fingers to the save key creates a copyrighted work. Once expression is committed to a tangible medium, copyright protection is automatic. So, postings of all kinds are protected the same as published printed works.
The saving grace: implied and express licenses to use internet materials
Whenever an author posts anything on the internet, he or she should reasonably expect that it will be read, downloaded, printed out, forwarded, and even used as the basis for other works to some degree. So, just by posting online, an author implies a limited license to use their work in this manner. Think about the rights a newspaper editor has to publish a letter to the editor. The author of the letter probably did not include a line in the letter giving the editor an express permission to publish the letter, but anyone who sends such a letter must be presumed to understand that this is what happens to letters to the editor.
On the other hand, most authors would not think that posting a work online automatically gives consent to commercial use of it without permission. This is not part of what one reasonably expects, and so it's not part of the implied license.
The trouble with implied licenses is that their boundaries are vague. Is the right to create derivatives in or out? What about large-scale nonprofit distribution? Implied licenses are vital to the operation of the internet, but they are not as good as express licenses, licenses that spell out in detail what rights the author of a work wants readers, viewers or listeners to have. You can easily give your works an express license by attaching a Creative Commons license to the materials you post online. It's easy and it sends the message that you want your materials to be part of the flow of creativity. No one creates in a vacuum. Just as you build on others' works, others will build on yours.
The role of fair use
Fair use plays a critical role in both research and teaching. It balances authors' rights to reasonable compensation with the public's rights to the ideas contained in copyrighted works. It used to be safe to say that reasonable analog educational, research and scholarly uses were fair uses, but some of those same activities in the digital world have been challenged. This is mostly because copyright owners have gone to great lengths to make the rights we may need to carry out research & teaching activities easy to obtain and reasonably priced through collective licensing (the Copyright Clearance Center, in particular). Still, the main cases in this area have involved commercial entities, so their application to nonprofit educators is far from decided. To the extent that fair use is less clearly applicable than it used to be, reliance on fair use for uses of works we find on the web can be bolstered by reliance on implied and express licenses. Where fair use may be questioned, implied rights may be broader, but an express right to use is best - it's clear and reassuring. It's possible today to search Creative Commons licensed works by license type, or limit your search to be sure that your results include only materials intended for use by educators and students.