Hi there, Philamom. Good advice so far, especially that bit about cleaning coins. Just don't do it!
There are many ways of finding out possible values for these coins, but all of them will require you to trust someone. A coin's value is based on its scarcity, its condition, and its grade. Grading coins is an art form, more than a science. If you are a complete novice, then I strongly encourage you to seek help from a pro to grade these coins. Even if they are in holders and are marked, the grades may be wrong. As I said...it's more art than science sometimes.
If you had just a few coins, the best way to get started would be with the friendly folks right here at the forum. With "boxes" of them, well, that get's harder.
Here's some questions that might help you at least get started:
1. Are these modern
US coins that you could likely find in you pocket change, or are they "old coins" that no longer circulate?
2. Are they silver (dimes, quarters, halves, etc. minted 1964 or earlier?) Nickels and pennies generally are not made of silver. If you have silver coins, even if they have little collector's value, they have "melt value" for the silver that will be many times face value.
3. Are any of the coins gold? If so, they, too, will have melt value many times face value. Gold is soft...so gold coins are easily damaged. Handle them carefully because a dent, ding or dimple can cost you hundreds to thousands of dollars if the coin is collectible.
4. Are any of the coins REALLY old (from the Civil War or earlier?)
Separate foreign from domestic coins. In the
US coins, separate old coins from current ones. Use a
Red Book to at least get a feeling for what may be valuable.
If you have a digital camera...you can post pictures on this forum; we can help give advice...
If there is a coin club in your town/city, you may be able to get help there, as wall. Coin shops vary dramatically from one to the next, but if someone you trust recommends a particular shop, they can help too.
Finally...if you think you've got a coin (or total collection) that is VERY valuable, proceed with caution if you choose to sell. Again, people on this forum can give great advice if and when you get to that point.
Best wishes...