Q. How are somebody, anybody, someone and anyone used?
A. Basically the same way some and any are used.

somebody/someone is used in positive sentences:
  It appears that somebody camped here last night.
  It appears that someone camped here last night.

anybody/anyone can be used in positive sentences when used as it doesn’t matter which:
   You can get just about anybody to smile by smiling.
   You can get just about anyone to smile by smiling.

anybody/anyone is used in positive sentences following never, hardly or without:
   It seems there is never anybody home during the day.
   It seems there is never anyone home during the day.
   With this cooler weather, there is hardly anybody on the beach.
   With this cooler weather, there is hardly anyone on the beach.
   A tree in a wilderness area could fall without anybody hearing it.
  A tree in a wilderness area could fall without anyone hearing it.

anybody/anyone is used in negative sentences:
   There isn’t anybody here.
   There isn’t anyone here.

anybody/anyone can be used in a positive sentence when the sense of it is negative:
   I decided not to loan them anybody from our team.
   I decided not to loan them anyone from our team.

anybody/anyone is used in questions:
   Does anybody really know what time it is?
   Does anyone really know what time it is?

somebody/someone is used in questions where we hope the answer is “yes”:
   Can somebody help me lift this heavy box?
   Can someone help me lift this heavy box?

somebody/someone is used in questions when offering or requesting:
   Could I please have somebody return my call?
   Could I please have someone return my call?

Q. How do the -body and -one forms differ?
A. You can find an explation of the minor differences here.