When purchasing a book, the more of the author's hand writing that is in the book, the more a dealer will usually charge. Lately there is about a $25 dollar difference in the price of two otherwise identical books. Your name, and the authors signature, uses more ink than the signature alone. The "To" before your name uses more ink. It they DATE the autograph, this is more valuable, and if a short sentence is written, well that is more ink. An inscription to someone famous, is usually worth a price hike, and the "Presentation" copy, which is usually a copy the author gave to the people it is inscribed to, can be worth $100. The dedication copy, of which there is seldom more than one, can double the price of a book.
Read the trade magazines, and the local newspaper for local conventions and books stores having author signing sessions. [My local Waldenbooks had an unannounced Esther Freisner signing a year ago, and I didn't find out about it until the day after.]
Keep a list of either the books that you want to get signed, or note the fact that a book is signed on the plastic bag or dust jacket protector of your book. Another way to mark the book is to put a thin white paper book marker between the front cover pages. I also suggest that you confirm that the book you are bringing to a signing session is NOT already signed.
When you go to a signing session, go early. It is better to wait a half hour before the session, than an hour on a line. You also meet the nicest people on those lines. Remember, they like the same book that you do.
Most signing sessions have some rules. The primary rule may be a limit on the number of books to be signed, or that books that have to be purchased at that store. Usually, if you purchase one book, you can get a second book signed. The number of books at these sessions is usually 3, but this may vary depending on how long a line is. There is seldom a restriction on your getting back in the line, though I have also had that happen. Please follow the rules.
Mark the page you want signed with either a white paper book mark or by tucking the dust jacket in the page. I prefer the white paper. I also like to use the title page (the one with the copy right information on the back) for signatures of author, editor and illustrator. Sometimes there is a title only page just before the title page. I only put signatures there if the page has the author's name, or if I need room for 2 or 3 signatures. For Anthologies I like to use the table of contents (I never did find a signature that was 'supposedly' somewhere in a book that I bought).
If you want a book inscribed to you, neatly print your name on a piece of paper. This is another good use for that white page marker. I suggest Pencil to write this, just to avoid ink blots. Don't get upset if the author is not doing any personalizing in books; several authors have problems that prevent them from long signing sessions.
Bring your own pen. The author will probably have their own pen, but just in case the reader prior to you just stole that, bring an extra. AND be prepared to give that pen away. I rarely use my "Andre gave me that pen" for signing, since I don't want to loose it. I don't suggest felt pens, unless you have tested it and it doesn't bleed through the pages.