A lot of people view supporting authors from a variety of ways. A lot would go to book signings, ordering bulk of their books at once, chatting with the authors on Facebook about how much they really enjoyed their book.
Here are the ways I support an author
1. Pre-Order Books
I like to pre-order books. Now I may buy the book but then I wait until I have the last book in my hands so I can read the series straight through. Some authors even have it as to where if you forward them the receipt of their book you ordered online they'll mail you autographed bookmarks, or some swag buttons.
2. Order the Hardcover or Paperback
I'm a college student so naturally my money is sucked up by the price of textbooks. Hardcover books tend to be expensive. So I end up just waiting for the paperback version to be released. Don't forget sales are everything. There have been times where the publisher has cancelled a book series because there wasn't enough sales, and they thought people weren't interested in the series.
3. Write Reviews
Review the books you've read. Now don't go on a long rampage on why you hated the book and thought it was the worst book you've ever read (believe me I've seen plenty of those) just keep your review simple, and professional as you possibly can. What you liked about the book, what you didn't like, then rate it.
4. Contact the author
Most authors are on Twitter, and really like it when a reader tells them they just bought the book, and really enjoy hearing compliments from their readers.
5. Recommend books to friends
When I read a book I really, really like I recommend it around. I love trading books with my friends which is why I like having paperback books. I swap books with my friends for the weekend.
Also in support of authors they have to do book signings. In order for them to do a book signing the bookstores have to stay open. Help keep bookstores open. For every book you order online through Amazon go buy a book at Barnes and Noble.