One of the first thoughts is a search of buyers in places where numismatists (coin collectors) to conduct transactions. However, the first time to establish the business does not always work. Need a good reputation as a supplier of coins to not be mistaken for the seller of stolen goods. In addition, novice diggers are often not able to correctly evaluate ancient coins. You need the experience. If you do and are neither a numismatist nor even the diggers, to evaluate existing findings, you couldn't even begin.
However, numismatic clubs basically exist in relatively large cities. If you are a hick, you come to the aid of the Internet. There you can find special auctions where you can sell old coins. You have the opportunity to set prices, focusing on catalogue. If no one has bought, just lower the price and again expose for sale their coins.
Coins can also be sold, finding all in the same Internet one of the numismatic forums. You can find them by driving in a search engine the phrase "numismatic forum" or something. The beauty of these online resources is that there you can not only sell old coins, but also to know the approximate or even exact cost, absolutely free. On these forums there are auctions where anyone can put their coins up for sale. If someone unknown value of the coin, this person is on the forum to create a theme from there posted a photo and asked to evaluate the coin. Knowing its value, you can put the lot up for auction.
Another good way to sell coins is to create your own website (even on free hosting). Specify the prices, as well as photos of coins, recommendations, terms of shipment. The address of your website, put in the signature of your profile on the numismatic forums to increase the number of potential buyers.