when do we use "among" and when do we use "amongst"?

There is a very minor difference between both the words. Among is a word used in our everyday life while amongst is a word of archaic English. It might although be used in British, Australian, and Canadian English, it is rare in American English. The -st at the end of amongst is a holdover from a period of English in which s sounds were added to words (usually nouns) to make adverbs. Other examples of words inflected this way include always, once, whence, etc.

Hope this helps!