Go to the bank. This method takes some patience but it works. Before 1964, all U.S. coins were made of a high percentage of silver so if you can find a quarter, for example, that was minted pre-1964, it is actually worth closer to $4 in today's silver prices. All you need to do is ask for rolls of quarters, dimes and nickels and check the dates. Keep the pre-1964 coins and return the rest for cash. Repeat.
Check online auction sites like eBay. Ebay has many auctions listed for old silver coins. Most of these coins consist of old silver dollars and other coins made before the 1950s when U.S. coins were actually made of mostly silver. Examples of these coins include the Peace Silver Dollar and the Morgan Silver Dollar. Regardless of their collector's value, these coins are worth approximately $12 apiece in today's silver prices. If in good condition and a rare date, they can be worth considerably more.
Go to local estate sales. Estate sales are like large garage sales and oftentimes you can find old coin collections that contain silver dollars and other old coins of high silver content.
Go to flea markets. Flea markets are good places to pick up old silver coins because coin dealers often have nowhere else to sell them, especially if they don't use the Internet. If you do go to one of these, it is a good idea to bring a coin guide like "The Red Book"–a coin collector's bible, to asses the value of the silver coins you find.
Shop for silver bullion coins online. Silver bullion coins of various dates can be bought in bulk. These coins come in various sizes but are sold at near-current market prices. Check the additional resources for reputable silver dealers.