As prepositions the difference between amid and among is that amid is surrounded by; in the middle of; in the center of while among is denotes a mingling or intermixing with distinct or separable objects. Among is considered less formal of the two. The word among should be used when it is followed by plural countable nouns or by a word indicating a separable group of people or things, congregation, crowd, etc, • The priest walked among his congregation, shaking hands with a few. Amid on the other hand is mainly used with uncountable nouns. It suggests that you are surrounded by something that is usually inseparable. • The three rebbers escaped amid the confusion that followed the fire.

Well, the difference is not so obvious that a native speaker (like me) can think of a simple explanation. "Amid" is very formal and old-fashioned. You won't hear it in daily speech. I'd expect to hear it at the start of a fairy tale or a documentary. "Amid" can be used to describe the middle of an action or event. This is the only time where you can't substitute "among" for "amid." But it's still very formal. I'd say "in the middle of" instead.

Most of the time, "amid" is placed at the beginning of the sentence. Among is placed before or at the end . For example, "Among the faces in the crowd..." "There was a face among the crowd." "Among" implies within ...