In any kind of work that you can cite, once you've identified what kind of work it is you need to figure out who wrote, recorded, or made it. The author is the person who you have to give credit to, and citing is all about giving credit for ideas and creations.
An important part of identifying the author is that authors do not have to be individual people. Most authors are people's names, but things can also be written by:
Since a reputable author is a critical part of identifying reliable information, when you're not sure who wrote something you should think twice about relying on the information in it.
Books are usually the easiest things to find the author on, because it's all over the cover, spine, and inside of the book. If it isn't on the cover, flip to the inside Title Page which has a bunch of information that usually includes the author. It may not always say "By" before the author's name; many books just name the author under the title and assume people will figure it out.
Some books have an editor instead of a single author. When you are giving credit to an editor in List of Works Cited entry you indicate they're the editor with (Ed.) after the name (or use (Eds.) if there's more than one).
Authors are usually easy to name in journal and some magazine articles; magazine columns and newspaper articles don't always have bylines though. Look at the top and bottom for credits that say things like "contributing" or "byline" to indicate who wrote it. If you can't find an author, you can look up the directions on citing an article by title in the MLA Handbook pages 156, 162, and 223 may help), if you are sure that the information is what you want even without an author.
When you're citing a chapter or article from a book, the author you want is the person who wrote that section of the book. If the book has a separate editor, you should write that down too though! You'll need both author/editors to do a good List of Works Cited. The author of the chapter, essay, or article is the Author that you'll use for in-text citations; if there's a separate book editor that name is only needed for the list at the end.
Web sites are the hardest to find authors for. Look at the top and bottom of the page. See if the web site is by a corporation or organization; if so that's probably the author. For example a Census statistic from the U. S. Census' home page is often cited with the author being the United States Census Bureau. Don't be afraid to give credit to a group of people if there's no name of a single person who wrote it.