Well, I don't have a grammar text which can give you general rules on the use of these prepositions .  However,  in general , when we are talking about locations are to be part of something  "in" usually meanings  "inside"  "  " I am in the school." " He was in the army " . "At" tends to be less specific about the exact location  .  " I am at the office " means that I am there generally , whereas " I am in the office" would be more specific about the location .  In practice , it  would mean the same thing. If I said, " I am at the hospital , now . " I would mean that I have just arrived there " at " the location . " I am in the hospital ,now" would mean that I am inside the building - but again you could use either to mean more or less the same thing. There are so many idioms with "in" and "at" that the best rule is to memorize . 

You also  use "in" with times of day " in the morning/evening/ afternoon"  but " at dawn " , " at sunset" ; In October/winter/autumn  

" In " the next sentence would be correct; "at the next sentence -incorrect" . He is at the football match vs He is in the football match - big difference - 1) means he is at the stadium  2) means he is playing in the game . 

"On" is a lot easier . Since we are talking only about "in" ,"at" or "on" as used for locations,  "on" refers the placement of something above or on top of something else . The hat is on your head , The food is on the table . The  cat is on the bed . 

Again, "on" has many other idiomatic uses " on vacation " . 

Last one, "in time" , "on time" , " at times" .-  They say that Mussolini made the trains run on time . ( they were never late .) Am I in time for the start of the game ? i.e. am I late or not?  At times  you make me crazy ! ( Sometimes /from time to time.)