That's right, not one thin dime!
Let me start with a confession: this is a self-serving post. I readily admit that and hope all my readers take the following action to help
me. But you can do these things for any writer whose work you like, and I encourage you to do so. Every little bit helps.
1. Tags - This refers to Amazon listings. If you view a book on Amazon you can scroll down past the reviews and find a section called "Tags Customers Associate with This Product." Books with lots of "agreement" on a tag will show up higher in search results for that term. Unless the term is "rubbish," "tripe," or "infantile," this is generally a good thing. There should already be several tags there as most authors will tag their own books. The way you can help is by agreeing with those tags. To the left of each tag is a box. Simply click inside that box and your "agreement" will be registered. But you're not done! There may be more tags hidden. On the example below, you can see the words "See all 15 tags." Click on this to reveal the rest of them (your page will refresh). You can also, if you like, add tags of your own. I would only recommend doing this if you've read the book, however, and are sure the tags are appropriate.

2. Likes - The next thing you can do while at a book's Amazon page is "like" the book. As with tagging, you do not have to have bought the book to like it. The Like button in next to the book's rating. Just click on it and you're done. It will change from a blue "Like" button to a orange "Liked" button (as seen below). This, as far as I can tell, doesn't help with search algorithms or anything like that but if a potential buyer sees that a lot of people "like" a book and it has a few good reviews, they may be more "likely" to buy it.
3. Facebook Shares - Attention-starved writers like me will post stuff about their books on Facebook. I know, weird, right? If you're a true blue friend or fan, you can share their posts to your Facebook friends. You don't even have to comment on it, just share it and it'll get more eyeballs on the book.
4. Twitter RTs - This is another easy one. Writers tend to Tweet about their books as well. I know! Just click that little Retweet button and your Followers will all get to see how weird your literary tastes really are:

5. Buy Free Books - Writers, being attention whores, will occasionally give their books away for free. Why would they do such a preposterous thing? Because it's not about the money but the art, and as long as people are reading our work, we could care less about turning a profit. No, wait... that's not it. It is about the money! And the best way to sell books is to give them away. If people read one book and like it, they'll hopefully buy more. It also gets our books on those Amazon Free charts and despite what that cop in Provo told me, exposure is a good thing. So when you see an author announce that their book is free, whether permanently or only for a day or two, go buy it. You'll help them out and, who knows, you might get something out of it, too: you might actually like the book! Part two of this is to review that book you got for free! It was free, it's the least you can do, right? Personally, I don't leave negative reviews. This game is hard enough. But whatever you do write, make sure it is honest and reflects your true feelings about the work. Review readers are notoriously harsh toward works that seem to have "fake" reviews attached to them.
So, I hope this has encouraged you to go support me...er... your favorite writer. Leave a comment with other tips that you know of for supporting writers for free!
Best,
Michael
Also read
5 MORE Ways to Help Authors without Spending a Dime.