Do you have silver eagle coins just laying around your house? Instead of letting them sit in a box, sell them and use the money for something useful.
Research the current price of silver. Silver eagle coins are valuable because of the amount of silver in them. Most silver eagle coins are one troy ounce of .999 silver. Never sell a silver eagle coin for less than the price of an ounce of silver. It doesn't matter what shape the coin is in, it is still worth money because of the silver content.
Call your local coin shop. Coin shops are constantly buying and selling coins. They will buy most of their coins from individual sellers like you. Call them and ask how much they would pay for such and such coin. Write the number down to compare it to other offers.
Search online auction sites. Online auction sites are filled with coins for sale. Search for the silver american eagle that you have and see how much it usually sells for on the auction sites. Compare this number to the coin shop offer.
Sell your american eagle coins to the highest offer. If you prefer to sell your coins locally then you can use the auction site prices as leverage against the coin dealer. Tell them that you conducted a little research and found that the average selling price is x amount of dollars and that they are offering you far less. They will usually raise their offer to offset the difference.