How can you tell if a quarter is rare?

Answer 1

That's a very broad question because quarters have been struck for over 200 years at four different mints. Virtually anything in current circulation with a date of 1965 or later is not going to be worth very much, except for a couple of state quarter errors - Delaware with the front and back both oriented the same direction, and Iowa with an extra leaf on the ear of corn.

For earlier coins, you'll need to do some research. I'd suggest getting a copy of the Whitman "Red Book" at your library as a good starting point for reading about the history, mintages, and values of U.S. coins.