Before a book is released for sale to the general public, early copies are typically sent to a limited number of people. These early copies may be called "galleys," "advance review copies," or "advance reading copies" (ARCs). They may have the final cover art, or they may be bound with a plain cover. These are the earliest copies of a bound book and are often the type of copies sent to reviewers.
These preview galleys or ARCs are actually more expensive for a publisher to print than the final copy of the book, in part because of the smaller print runs. Because of this, some publishers are limiting the number of advance copies they produce. If you want to be one of the few people to receive an advance copy, consider what publicity you can offer to the publisher in return. Writing a widely read blog about books, writing reviews for local newspapers or specific trade journals, or finding other ways to communicate with large numbers of people about books are all possible platforms by which you can provide some marketing for the publisher's benefit.
You can become involved in reviewing ARCs by joining a group blog, adding your book review blog on a "blog book tour" or signing up for online reviewer programs such as those at Goodreads and Library Thing. Subscribe to publishers' mailing lists to learn about upcoming releases and how reviewers may access ARCs.
If you have an idea of how you can provide publicity for the book, it is possible to contact publishers directly to ask for an advance review copy. Before considering this route, do your research and focus your inquiry on one book you really want. Contact the publisher via its website and state your case for why you would be a worthy recipient of an advance copy to preview. Above all, be professional in your correspondence. Do not be offended if the editor declines your request. As publishing houses tighten their belts, the practice of printing a large number of ARCs is falling by the wayside. Be aware that you may be required to sign a confidentiality agreement stating that you will not publish or disseminate material from the book before its official release date.
You may also inquire at local newspapers, hobbyist magazines or professional journals and volunteer to review new books for them. Academic publishers send new books to many academic journals in hopes of obtaining a review. The journal editors, in turn, may send the new books to willing reviewers. The volunteer reviewer writes a book review, which will then appear in the academic journal.