I'm going to do a separate post about what authors can do to promote their books, but since I'm a very avid reader, I wanted to share a few ways you can help your favorite authors very easily. Aside from buying their books, which obviously helps them.
1. Tell the author you liked their work.
Writing is lonely. You don't always get feedback, and sometimes when you do, it's the people who hated your work the most who will be more than happy to share that. Yes, writers want to sell books, but that's the business side. The person/creative side is happy when someone genuinely engages with their work. That doesn't have to mean you fawn over it and tell them they are the best author ever. You might even disagree or grapple with a concept. That's fine; as long as you're reading their work and have something to share, I'd take a wild guesstimate that 99% of authors would love to hear that. If it feels weird to send a fan email, do it via Twitter. I've interacted with lots of my favorite authors, like mystery author Sue Ann Jaffarian (@sueannjaffarian) and paranormal YA author Tera Lynn Childs (@teralynnchilds) and not only do I get excited when they Tweet back to me, but 140 characters is less intimidating than an email, and unless they're Stephen King level of famous, they are probably going to read what you Tweet.
2. Like their book on Amazon.
This literally takes a second and looks good for the author. (Note: I don't 100% understand what it does for their book's rankings on Amazon, if anything, but still, if 100 people have liked a book, that surely counts for something with potential buyers.)
3. Review the book on Amazon, Bn.com, Goodreads, etc.
Reviews don't have to be long or eloquent to get the point across. You think ___ is like ___ on acid? Or __ is a beach read page-turner? It's all good.
4. Request your local library and bookstore carry the book.
This one requires a bit more effort, but goes a long way. You might even find that you turn the librarian or bookseller on to a book, and they in turn may tell others, and also may recommend books to you.
5. Share your love of the book on Twitter, Facebook, etc.
Often this may simply mean you retweet or repost something the author has posted; it's that simple. You may also find them holding contests, posting about events, or offering up recommendations for what to read next, or giving sneak previews of their upcoming work.