"I have an old book"
When it comes to books it is a good idea to recalibrate your definition of the term, "old". In terms of books, any book printed after about 1900 would not be considered old. In fact, most in the rare book world would not consider books from the 1800s to be very "old" either. To most, an "old" book would be books from the 15th century up to the 18th century at the latest.
The age of a book is only useful in the sense that it can help determine rarity. Remember, you're looking for a combination of importance, rarity, and demand. A book that is printed in the 1600s is not necessarily important or in demand; however, the age indicates that the odds are higher that it is rare. A good, if general, dividing line is to separate books printed before 1800 from those printed after 1800. After 1800, printing and book-making became more advanced, and thus books were printed in larger numbers and often with cheaper materials. In other words, a book printed prior to 1800 is more likely to be rare whereas books printed after that date are more likely to be relatively common.
"Nothing is more common than a rare book"
Many books are rare. Often, a book is rare simply because the author was an unknown and the publisher (wisely) printed only a small initial run of copies. In other words, the book may be rare because it just wasn't a good book. In the absence of some importance or demand, there isn't often value.
What makes a book "rare?" It's not enough to simply count the number of copies printed or available. It's easy enough, if your books are printed prior to the year 1800, to say they are rare in that the quantity would be limited. But for books printed post-1800, it isn't so easy. This is especially true for books printed post-1900. Let's take Ernest Hemingway's For Whom the Bell Tolls as an example.
When a book was produced in large numbers, rarity is found only in Condition and Edition. A copy of For Whom the Bell Tolls is extremely common. A copy printed in 1940 (the first year of publication) is also fairly common. A first printing is less common but still not all that rare. A first printing in the original dust-jacket is a little less common. A first printing, in the original dust-jacket, in nice condition (largely appearing unhandled and unread) is somewhat rare. So, you have an important work, in high demand, in a rare state and condition. This book would likely bring around $500 at auction. The same book lacking the jacket is worth $10, because it isn't rare in that condition.
What else can make a book rare? Illustrations and/or limited editions. Some of the more valuable books printed during the 20th century were limited edition books with color illustrations, often signed and numbered by the artist. Going back into the 1800s, some of the more valuable books contain hand-colored illustrations (such as atlases with hand-colored maps.) Often, you can know if a book is rare just by looking at the book itself. If the book contains hand-colored maps or illustrations, for example, you can be somewhat confident that not may were produced because producing such a work would take a large amount of time. Or, you may pick up a book that is in an obviously expensive fine-binding. Again, you can be confident that not too many were produced because it would be very expensive and time-consuming to do so. It could be the quality of the paper used, or it could be the visible quality of the printing.
Remember, none of these things mean that the book is important and/or in demand, but at least there is a good chance it is rare.