NOTE: Amazon has updated their terms of service for reviews on Oct 3rd 2016.
They honor giving out review copies of your book, but not as an incentive for a positive review. It's a little vague and confusing, but they want to avoid people getting free stuff for positive reviews.
You may give out review copies of your book, but no longer in direct exchange for a positive review.
Readers that choose to review something can do so on their own. Without your prompting or influence.
Amazon is being vague so play it safe and use Amazon's "wording" directly when soliciting for a review. Example:
Attached is a review copy of my book. It's the first in a fantasy series about two warring elf nations. Hope you like it!
Notice I kept it short, and didn't even request a review. Provide your book as is. Let the reader decide what to do with it.
NOTE: Never offer them money or any type of incentive. NEVER EVER. They will block you or worse report you to Amazon. Amazon allows you to give out review copies of your book. Always check with Amazon for the latest in review policy (it changes frequently).
Also NOTE: Depending on your email program you may need to remove the name before the actual email manually.
These are publicly available email addresses openly looking for review solicitations. These email address are listed on forums, Amazon account profiles, review blogger sites, etc.
Also these guys all review books, regardless of their name (like "productReviewguy"). Email them all!
The future of your book depends on how it’s published. The way it performs the first few weeks to a month gives data to Amazon telling if it’s either a best seller or a flop.
The number one factor Amazon measures is sales. The more sales you can get, the better. Amazon’s system doesn’t separate free books from books purchased at cost.
At the minimum, you must give your book out for free for five days using the Kindle Direct Publishing five day free promotion, which is available every 90 days. Statistically, books priced at $0.99 sell better than other prices. Pricing your book higher lowers the amount sold. The first month it’s best to price it at $0.99.
If your book is slow to gather reviews, use Amazon approved methods such as:
One of my favorite quotes is from George Bernard Shaw who said, “The reasonable man adapts himself to the world; the unreasonable persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man.”
Writing books as a self-publisher depends heavily on writing books that are reasonable, however. You want to write books that people want and are searching for. If people aren’t searching for it, then they won’t find it (without marketing). Writing a very unusual book as a self-publisher makes the chance of people finding it slim. However, everyone writes books people are searching for, so you need to be unreasonable just enough to stand out from the others (niche).
Write a book people are searching for (reasonable) that stands out just enough to generate attention, pulling customers away from the mainstream (unreasonable).
Find the balance to be both reasonable (to be easily found), and unreasonable (to stand out).