ON
- to express the surface of something:
(e.g. "The book is on the desk.")

- to specify days/dates:
(e.g. "Let's meet on Wednesday." / "Let's meet on 23rd of April.")

- to express someone using a device, or something in a device:
(e.g. "She's on the phone right now." / "My favourite song is playing on the radio!")

- to express a part of the body:
(e.g. "He slapped me on my cheek.") 

- to express the state of something:
(e.g. "The stove is on fire!" / "These clothes are on sale right now.")

AT

- To specify time:
(e.g. "Let's meet at 4pm later.")

- To indicate a place:
(e.g. "He's at the hospital.")

- To express an activity:
(e.g. "He threw a ball at me." / "I'm not good at playing chess.")

IN

- To express unspecific time:
(e.g. "He drinks coffee in the morning." / "The order will arrive in 2 weeks.")

- To indicate a specific place or location:
(e.g. "He's in the kitchen.")

- To express a characteristic (shape/size/colour):
(e.g. "We gathered in a circle." / "Does this shirt come in other sizes?" / "Does this shirt come in black?")

- To express while doing something:
(e.g. "In preparing for the exams, I stayed up all night to study.")

- To express an opinion/interest/belief/feeling:
(e.g. "I believe in you. You can make it!" / "I'm not interested in religion."

Into and onto are used only with verbs showing movement. They show both the direction and the result of the movement. In and on are used with verbs showing movement and verbs not showing movement.

(e.g. "He dived into/in the river." / "He threw his bag onto/on the floor")

(e.g. "He said the water in the river was cold" / "He said his bag was on the floor.") (you cannot use into and onto in these cases because "said" is not a verb involving movement.)