You should always provide the source or author, unless specifically stated that it is is not needed to do so, such as under certain licenses.
Here is an example license of xkcd.com:
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License.
This means that you are free to copy and reuse any of my drawings (noncommercially) as long as you tell people where they're from.
That is, you don't need my permission to post these pictures on your website (and hotlinking with is fine); just include a link back to this page. Or you can make Livejournal icons from them, but -- if possible -- put xkcd.com in the comment field. You can use them freely (with some kind of link) in not-for-profit publications, and I'm also okay with people reprinting occasional comics (with clear attribution) in publications like books, blogs, newsletters, and presentations. If you're not sure whether your use is noncommercial, feel free to email me and ask (if you're not sure, it's probably okay).
Generally it is possible to use parts of a source without having digital right concerns. For instance, you can post one frame of the comic with the link to the source where the full content can be watched. Or you can quote a sentence. You can upload a part of a movie. What you can't do is displaying it as a whole in full quality. By using only a part and providing the link to original source you may actually benefit the original author. When in doubt you should ask the original author for permission.
For example, an XKCD comic does not need permission as long as it's not for commercial use. So, you cannot use it for printing T-shirts, but you can use it for educational purposes. In the description of the picture it is a good idea to include the author or source.