As a long time numismatist (fancy word for coin collector), it can actually get very complicated!
Keeping it simple 3 things will determine how much your coin/bill is worth. Condition, rarity and collectability. Condition are acutally assigned grades and can vary from barely recognizable date up to mint, uncirculated. Rarity is a combination really of how many printed/minted and how many are believed to remain (for example, on your silver certificates, you used to be able to redeem them for silver. Those redeemed by the Federal Government were removed from circulation so just printing numbers dont tell you the whole story). Collectability is the third key. It explains why one may have a rare coin in very good condition but not worth as much as a different coin which is not as rare nor in as good conditon.
Here is one example to show just how the three come together and how complicated it can become. A 1909S VDB Lincoln penny (S means minted in San Francisco and VDB mean the designers initials which not all 1090 S had), in good condition (which is the lowest condition recognized meaning the coin is well worn and the date barely visible), will sell for about the same price as a pristine, uncirculated 1855 US silver 3 cent piece will! Why? Lots of folks collect Lincoln pennies and the 09S VDB is a key to the set. Few collect the 3 cent series.
Ok, what to do. One easy start is to get ahold of "A Guide Book of United States Coins" by R.S. Yeoman. Almost any library of any size will have this reference. It is updated each year and continually printed since 1946. There you will find a good explanation of how to roughly grade each coin as well as value in the various grades. HOWEVER those usually represent retail prices. Selling to a reputable dealer you can expect in the neighborhood of 25-40 percent of that value. Also recognize that even common date silver coins can be fairly valuable for their bullion content alone. Phone book good place to look for dealers and NYC at least used to be a hotbed of some pretty impressive firms.
A Guide Book of United States Paper Money by Arthur Friedberg is the equivalent for your silver certificates, works the sames, and frequently can be found in a library.
Failing all that fall back on the kindness of others
When my brother-in-law wanted to liqudate coins he had accumulated he gave them to me. I researched them and sold them at a regional coin show to a dealer I knew. Perhaps asking around you might find a friend or acquaintance who might do the same.
Now, sorry you asked?
