For book collectors, a volume signed by the author is often the most treasured part of their collection. Owning a book that the writer held in his hands (if only long enough to scribble their autograph) gives a sense of connection between novel, writer, and reader that goes beyond the story contained within the covers. At least in part because of this, collecting signed first editions has become a specialty within the book collecting community which has exploded in recent years.
Before going into specifics about signed books, a few brief thoughts on book collecting in general are important, as they affect the value and desirability of signed books as well. With nearly any collectible (and books in particular) condition is always key. A book in poor condition is almost never valuable, and for modern editions the dust jacket must also be pristine. Furthermore, first printings of first editions are generally the only ones of interest to the collector. Simply check the copyright page for the words "First Edition" at the bottom and/or a number sequence starting with a "1." Finally, when speaking of first editions and first printings, this always refers to the hardcover edition.
From a strictly financial standpoint, signed copies will almost always be worth more than unsigned copies, so in most cases you can expect to pay a higher price for these volumes; just remember that the rules regarding condition and edition outweigh almost any autograph. In other words, while a signed first printing of "Booked to Die" in Fine condition can be worth well over $1000, a signed copy of a sixth printing in Fair condition will likely be worth less than the original cover price. Also remember that signed copies of books by an author who is popular today may be over-inflated, and could easily drop significantly in value as time goes on.
Perhaps the best way to collect signed editions without any cost beyond the cover price is to attend signings by the author where you can have them signed for free. Many authors, particularly in the mystery genre, will do book signing tours every time they release a new novel; details can be found on either the author's website or the website of the publisher. They will also typically sign copies of their previous books, but check with the bookstore holding the event first. A common rule is that you can bring in a certain number of your older copies, but you must buy the new book at that store to have all of them signed (booksellers have to earn a living, after all).
If you don't live in an area that is usually visited by authors on tour, another way to collect signed first printings is to join one of the clubs offered by several independent mystery bookstores around the country. For example, both The Mysterious Bookshop in New York City and Poisoned Pen Books in Scottsdale, Arizona offer book clubs that enable member to receive signed books (chosen by the store's staff) by mail on a monthly basis. These range from debut novels by a new authors to specific sub-genres like British mysteries. The biggest advantage here is that you get the knowledge of an experienced staff and still only pay the normal retail price for the book. Most of these signed books won't skyrocket in value, but some will; Tana French's 2007 debut "In the Woods" now sells for over $150.00.
Some authors will sign and return copies sent to them (even Hemingway was known to do this), but this happens far less often today than in the past, and is far more likely with new authors than established ones. Always check with the author or their publisher before sending anything, always send return postage, and bear in mind that every time you ship a book, even for as good a reason as this, you risk it being damaged during the shipping process.
If you are collecting older signed books (particularly by authors who are no longer living) the process becomes more complicated. The proliferation of so-called booksellers on the Internet has both artificially driven up prices for these works and made the phrase "buyer beware" more critical than ever, yet the diminishing number of brick-and-mortar rare bookshops often makes the Internet the only option. If you must go this route, check out sites like AbeBooks, and whenever possible only buy from dealers who are part of the Antiquarian Booksellers Association of America. These tend to be exponentially more reputable than those you will find on eBay. Always ask for both detailed publishing information and photographs of the outside of the book, the copyright page, and the signature itself.
In the end, collecting signed first editions should be viewed in the same manner as any other hobby that borders on obsession. If you're doing it in the hopes of getting rich, it would be better to simply buy a lottery ticket. If you're doing it because you love books and respect their authors, it can be one of the most rewarding endeavors of your life, and can be a legacy passed down to future generations.