Where to sell your stamp collection depends on such factors as the value of the collection, whether or not you want to sell it yourself, whether you want to sell it piecemeal or as a collection, and the amount of time you are willing to wait to receive any possible payment. You may choose to sell your stamp collection in an auction, to a dealer or even to a pawnshop.
Before you decide where to sell your stamp collection, your first step should be to find out its value, either by researching via Scott Catalogues or through a reputable stamp appraiser. While taking your collection to a stamp dealer may seem like the easiest option, it is also not likely to net you as much as you could get through other options, as stamp dealers are in business to resell what they buy at a markup.
Depending on the value of your collection, you may choose to use an auction house. Be sure to choose one that specializes in the type of stamps you are selling. Another option would be to sell the stamp collection yourself using an online site such as eBay. Either way, you should come up with a reserve, or minimum amount you are willing to accept, before you begin. Keep in mind as well that you will often owe listing/auction fees no matter which service you use, regardless of if the items sells or not.