When people find coins, they do one of two things: place them in their collection or get the value of the coin and attempt to sell it to other collectors. Usually, getting the value of a coin is complicated. You have to factor in the year of the coin, how many scratches it has, if there are any errors (and if those errors happen to be rare), and any mint marks on the coin. When it comes to older coins, it gets even more complicated because bullion values, demand, rarity, and various design values start coming into play.
First off, the only safe way to finding the value of old coins is to bring it into an expert collector who has been examining the markets for a very long time. Only he/she will know exactly which marks give what value, which years are more valuable, or how special a certain error is. The tricky part about determining value is to believe not what you would pay for it, but what others would pay for it. It's very easy to both over and underprice coins by not understanding this concept.
A very popular factor is rarity, especially in old coins. Because older coins are obviously not in production any longer, more and more are lost or misplaced each year, reducing the number of specimens in existence. Nobody knows just how many exist of each exact coin, but the rarer they are, the more they cost, often times regardless of how old the coin is. Thousand year-old Chinese coins can be worth less than fifty year-old rare error coins because the former is actually very easy to find, while the latter can be worth thousands of US dollars.
A common practice among the black markets of the coin collectors is to offer services where scammers value the coin at a significantly lower price than actual worth, and then offer to purchase the coin at a higher price. They claim that the owner will have a hard time getting rid of it, and will snap it up at a lower price. Be careful of this and related schemes. It's sometimes worth it to get the opinion of multiple people; someone once sold a coin for $5 when it was actually worth $150 because she failed to ask someone else.
Since old coins are now becoming more and more in demand, you must take care when finding the value of old coins. There are guides here and there on roughly how much each quirk about the coin is worth, but only an expert with market experience can give you a straight answer on how much that coin of yours is worth. Most experts won't charge you anything, either, so it's safe to ask them.