I spent 29 years enforcing rules for a living, so it says something that the rule most new self-publishers unknowingly break isn't obscure at all: since 2016, Amazon's guidelines explicitly prohibit offering a free copy of a book in exchange for a review. Not payment specifically — any compensation, including a free copy given on the condition or expectation that a review follows. It's an easy line to cross by accident, usually by a well-meaning "here's a free copy, I'd love a review if you enjoy it" message that reads, to Amazon's systems, as exactly the kind of incentivised review the rule exists to stop.
What's actually allowed, and works: Advance Reader Copy programmes through a service like BookSirens, Booksprout, or StoryOrigin, where copies go out with no review obligation attached at all — readers who choose to leave one do so entirely voluntarily, which keeps it inside the rules and, honestly, produces more genuine reviews than a transactional exchange ever would. A simple, unconditional request in a book's back matter — "if you enjoyed this, a review helps other readers find it" — with nothing offered in return, is also entirely fine and is the single highest-converting review request I use across every book on this site.
Genre reader communities are worth more than most marketing advice credits them for. Readers already active in Facebook groups, subreddits, or Discord servers built around your specific genre are readers who review things they read anyway, as part of how they already engage with books — you're not asking them to do something new, just letting them know your book exists.
What I'd actively avoid: asking family or close friends to review, which Amazon's guidelines also treat as a conflict of interest regardless of whether anything was traded for it; review swaps with other authors, which sits in similarly grey territory; and anything resembling a review-for-review arrangement, no matter how organically it starts.
On the reviews themselves once they arrive — a debut's first handful will usually include at least one three-star review, and that's normal, not a crisis. Don't respond publicly, don't get defensive, and don't let one review shape how you write the next book. The reviews that matter for discoverability are the aggregate, not any single one, and an author account visibly arguing with a reviewer does far more damage than the review itself ever could.