You have just found a box full of stamps, or some loose stamps in an envelope, and you would like to know how much they're worth.
First, I must point out that there are over a half million different stamps out there. So, there is no very simple rule for finding the prices of them. I will give some quick guidelines, then refer you to a catalog to find out more.
Common stamps are worth 2 to 5 cents each, realistically. VERY common ones (the ones everyone has piles of) are about a penny each. When stamps are first issued, mint (unused) copies are worth face value (whatever price is printed on the stamp).
As a general rule, older stamps are worth more than newer ones, and mint stamps are worth more than used (cancelled) ones, but there are exceptions. Used stamps with high face value are generally worth more than used stamps with low face value.
Here are some commonly asked questions:
Q: What makes a stamp valuable?
A: A stamp is "valuable" if it exists in fairly limited supply, and there is a lot of demand for it. Most stamps from 1890 (for example) were printed in quantities of about 20,000 to 100,000; and many have been destroyed since then. In contrast, Most US stamps of 1995 are printed in quantities of 100,000,000 or more, with over a BILLION Christmas stamps printed each year! The quantity available is one of the most important factors in the prices of stamps. Stamps where only a handful are known to exist regularly sell at auctions for thousands of dollars apiece.
Q: How do I find the value of a certain stamp?
A: In the USA, Check your local library for Scott's Standard Catalog of Postage Stamps. These catalogs show retail values, and are updated every year. Stamps are organized by country, in the order they were issued. Up until 1997, the catalogs had former British colonies in volume 1, with the rest of the world in volumes 2 through 5. In the catalogs, the first column gives the price for a mint (unused) stamp, and the second column gives the price for used (cancelled) stamps.
Q: How do I find out when a certain stamp was issued?
A: Most newer stamps have the year of issue printed under the bottom of the stamp design. Use a magnifying glass. If a stamp is cancelled, check the date on the postmark; most stamps are used within 2 or 3 years of being issued. If a stamp has a date in the design, note that stamps are issued to commemorate 10th, 20th, 50th, 100th (etc) anniversaries of events, and this date is usually the date of the event being honored. Knowing when a stamp was issued will certainly help you find the stamp in a catalog. The very first regular postage stamp was issued in 1840, so you won't find any stamps older than that. ;-)
Q: What else should I look for?
A: There are lots of other things to think about. A mounted collection of stamps will be worth more than the same stamps piled in a box. This is because a properly mounted collection helps preserve the stamps better, and makes it easier to identify them. After a while, loose stamps may get stuck together. Some stamps are collected in blocks of 4 or more, or strips of 5, or whole sheets -- it's best to leave them the way you find them; don't pull apart blocks. Especially for very old stamps (before 1870 or so), some collectors will pay premiums for nice blocks, because so few blocks have survived.
Q: What if want more information?
A: Consult a stamp dealer if you have other questions. These days, you could also go to an auction site like EBay to see if anyone is selling similar stamps, and see what they're selling for. Many of the people selling stamps on EBay are stamp dealers who may be able to provide more information. Note that most stamp dealers get frequent questions about very common stamps. The more you know about your collection, the better off you will be, even if you're not planning to sell it anytime soon.
Q: I have an Elvis stamp ...
A: This one comes up a lot. The Elvis stamps printed by the US Postal Service are worth 25 cents, or 29 cents. Whatever it says on the stamp. Hundreds of millions of copies were printed. They are not rare. They are postage. Use them on your mail. If we used them all up, then the few that were left would have a slim chance of being valuable many decades from now. 2015: Oh, look, they just printed another Elvis stamp. This one is a "forever" stamp, so it's worth whatever the current cost of mailing a letter is.