The website is straightforward, and so are the sumission guidelines:
The Science Shelf seeks reviews or short notes recommending science books, even those already included on the site. Science Shelf readers deserve more than one perspective whenever possible. Reviews are generally positive or mixed, but negative reviews will be considered.
LENGTH: 100-1,000 words
RIGHTS: Nonexclusive electronic rights (you keep the copyright and earn a byline)
SUBMISSIONS: By email as text in body of message
GUIDELINES: The main rule for submissions is this: The goal of The Science Shelf is to connect science readers and books. Therefore, reviewers should view the books through the eyes of the authors' intended audiences, even if they personally would prefer a book written for a different readership.
Thanks for your interest!