When a new book is announced but not yet released:

1) Pre-order it. This is a variation of buying the book—if you are going to get the book anyway, please consider pre-ordering instead of waiting until the book is out. You can pre-order via your your favourite independent bookstore or via an online bookseller. Why? Pre-orders count toward first-week sales. A big first week bump in sales could put the author on a bestseller list—or at least make their publisher sit up and notice.
2) Request it at the library. If you're a library user, you can contact your library and make a request for the book. Why? The library would ask the publisher for an early copy, read it and hopefully recommend it to library users once the book is in the library system.
3) Add it to your Goodreads list. If you’re on Goodreads, find the book and click the ‘Want to Read’ button. Why? It’s like voting. If a book gets enough of those Want to Read votes, it gets on lists that Goodreads promotes to other readers. Want to Reads builds buzz for the author but it also lets you in on Goodreads contests, giveaways, or discounts the book becomes available.
4) Review it on Goodreads. Amazon doesn’t allow book reviews before the release date but Goodreads does. If you get an advance reading copy (ARC), rate and review the book on Goodreads. Why? Because your review really does make a difference. A written review with a rating is best, and you can be very brief, just a sentence or two. If you’d rather just rate the book, that’s helpful too.
5) Help build buzz via social media. The author will be sharing news about the book such as: cover reveal, excerpts, and early reviews. Repost and retweet. Why? Social media is like online word-of-mouth. When you share, you’re endorsing the author.

Once a book is released:

6) Buy the book if you haven’t already. For yourself and as gifts.
7) Tell your friends. Why? Most people buy books based on recommendations from friends. This is good old-fashioned word-of-mouth.
8) Check out or place a hold at the library. Again, you don’t have to buy the book to be supportive. If you’re a library user, borrow the book. If it’s already checked out, place a hold on it. Why? Holds indicate interest and lots of holds often motivate the library to order more copies.
9) Review book on Amazon and/or Goodreads. This one is so important, especially Amazon. Again, this can be just a brief line and a rating. Why? The more reviews there are for a book the more visibility it gets from those Goodreads and Amazon algorithms – meaning they’ll suggest it more often to people who are likely to buy it. Much as we'd like to think that word of mouth works best, this IS the new word of mouth. Amazon gets more eyeballs by far than any other book recommendation channel and Amazon's algorithms are set up so that the more reviews a book gets, the more often it pops up on lists and recommendations. You know those "if you liked this book, you will love ..." lists? Those "other people who bought this book also bought ..."? There is the magic 50 threshold and after that the magic 100 threshold where more good things happen, all driven by software.
10) Talk about it with your local bookseller. Even if you bought the book elsewhere or borrowed from the library. Why? Booksellers like to know what their customers have enjoyed. This could prompt them to read the book themselves, and if they like it, put it on the Staff Picks shelf. This is great exposure for a book – most customers browse Staff Picks.
11) Build buzz on social media. Why? This amplifies what the author is doing on social media. Hopefully you already follow the author on social media. So (1) Repost, retweet what the author posts or (2) Write your own posts about the book or (3) Do book selfies. Yes! Take photos of yourself with the book, the book beside a cup of tea, the book beside your cute kitten. It’s less work than writing a book review but you’re still getting the message out that you’re enjoying this book.
12) Write a book report and/or interview the author. If you’re a blogger, this would be awesome. Why? Because this introduces the  author to your audience. Interviews where you supply the questions are often better than a wide open ‘Would you like to write a blog?’. You know your audience and what they would find interesting so your questions would elicit that information. It’s also easier on the author to respond to questions than to compose something from scratch.
13) Nominate the book for an award. This could be for Goodreads Readers Choice awards or a local newspaper’s contest. Why? If for no other reason, it gives the author something to celebrate. And who knows – the book could go really far.
14) Recommend it to a book club. If you’re in a book club, recommend the book. Some bookstores offer book club “packs” for a discount. Sometimes publishers also offer discounts to book clubs. If you don’t belong to a book club, talk about the book to a friend who does. You can also talk to your local bookstore – sometimes they run book clubs and appreciate customer recommendations. Why? Wider exposure, multiple sales potential.
15) Ask your library if they can provide a book club “pack”. If a lot of people in your book club use library copies, request your local library to make up a book club “pack”. Why? More sales. And with the popularity of book clubs, we are seeing more and more titles bundled in multiples so that book clubs can check out the pack for all their members to read at the same time.