Ask the Author
Find the author's website, blog or social networking site, such as Facebook and Twitter. See whether she's posted information about upcoming releases.
Visit regularly and leave comments to her updates. Your goal is to establish a relationship with the author or at least make her familiar with your name. If you are an established reviewer, you can probably skip to step 3.
Send a polite email to the author, asking whether you can get an ARC when copies are available. Authors are eager to generate prepublication buzz for their books, so your chances are good as long as you can be relied on to spread the word.
Ask the Publisher
Find out whether the publisher maintains a blog. If so, it may offer ARCs of upcoming publications to its readers, so visit often to learn what books may be available.
Visit the publisher's website. Many publishers maintain "early readers" communities, and will make ARCs available to active members.
Find the FAQ page on the publisher's website. Often, it will include information on obtaining review copies, with a phone or fax number to contact. Don't be dissuaded by "professional reviewers only" statements--with the exception of certain big-name authors, most publishers will take all the free publicity they can get.
Use the publisher's contact form if no information is provided on its website. Send a politely worded e-mail with your request. Be sure to include the author's name and the title of the book you are requesting.
Read Shelf Awareness, a daily newsletter that contains ads for ARCs available from publishers. Just follow the link to collect.
Join an online community, such as Library Thing's Early Reviewers, which distributes ARCs to members.
Visit book review sites and blogs. The contributors to these sites frequently give away copies of ARCs they have received for review.
Befriend your local bookstore manager. Bookstores often receive ARCs from publishers trying to convince them to stock new books and the manager might be willing to share some of the loot.