Is "what am I to do" be commonly used in daily lives? Also what do following sentences imply? What should I do the next? What am I to do the next? Please.
closed as not a real question by J.R., MετάEd, Brian Hooper, RegDwigнt♦ May 18 at 22:46
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"What am I to do?" is roughly equivalent to "What should I do about this?" where "this" is some kind of problem you have, specifics to be understood from context. It is not commonly used anymore, but will be understood by native speakers.
Native speakers of Standard American English (and I think also Standard British English) never say "the next" without anything after "next". (They might say "the next person in line", or something like that.) Therefore, your other two sentences would be considered incorrect in those dialects. If you drop the "the", they become correct: "What should I do next?", "What am I to do next?"
Like "What am I to do?", "What am I to do next?" connotes that you have a problem you're trying to deal with, and sounds a bit archaic. If you are instead asking for instructions, e.g. for your next task at work, "What should I do next?" is the correct choice in StdAmEng.