Finding ancient coins is not common. You really have to know A) where to look, and B) travel to those places to look for coins. The only other way, and quite honestly, the easiest way, to acquire ancient coins is to find someone who owns a few and buy from them.

Otherwise, you will be hard-pressed to suddenly find a rare and ancient coin just laying around on a Greek beach. If you want to go hunting for ancient Greek coins, you could look in some of the most ancient of places in Greece using a metal detector or volunteer on an archaeological dig somewhere in Greece. If you do happen to acquire some ancient drachmas that you are allowed to legally keep and take home from Greece with you, you should know what they might be worth. 

The Older the Better

The older the Greek coin, the better the value may be. Some ancient coins date back over three millennia, although such finds are so extraordinary you probably will not be allowed by the Grecian government to keep them. If you are lucky, the Grecian government may offer you a "finder's fee" in exchange for allowing the found coin to remain in its native land. Still, the older the coin, the greater the value the coin typically has. 

The More Well-Preserved the Better

The thing with coins is that age has a way of eroding their surfaces. Most early drachmas were just metal or wood coins made from certain shapes. Later, faces of Grecian rulers were stamped on the coins. What you want is a nice hard edge with little rust, erosion, and/or corrosion to the coin, and if it has an image of a ruler stamped on it, the face's features should still be quite visible. If the coin you find or purchase from a seller/owner of ancient coins has all of the requisite features, including age, you have quite the treasure worth buying and owning. 

Getting the Coin Appraised

The owner/seller of an ancient Grecian coin has probably already had the coin appraised for value. If it is worth a lot, the appraisal would have been necessary for insurance purposes. However, these coins can grow in value the longer they are kept safe in a vault or safe, and the more rare they become. Before you purchase an ancient Grecian coin, be sure to have an art historian and a rare coin appraiser both look at the coin to get an idea of its true worth and whether or not the seller is offering you a bargain. 

For more information about ancient Greek coins, talk to a coin appraiser or stores that sell antique coins.