Between is with two people or things. Note the combination tw in a number of words meaning "two" such as two, twice, and twin.
Among is used when discussing three or more people or things.
Examples: She had to choose between licorice and cherry.
She had to choose among licorice, cherry, and lime.
Between is used with and. From is used with to.
Never use to with between.
Incorrect: We shuttled between New York to Chicago.
Correct: We shuttled between New York and Chicago.
We shuttled from New York to Chicago.