What is PREPOSITION?

The name "preposition" (pre + position) means "place before".

A preposition describes a relationship between other words in a sentence. 

Prepositions usually come before another word, usually a noun or noun phrase. 

Prepositions of time

English	Usage	Example
on	days of the week	on Monday
in	months / seasons time of day year after a certain period of time (when?)	in August / in winter in the morning in 2006 in an hour
at	for night for weekend a certain point of time (when?)	at night at the weekend at half past nine
since	from a certain point of time (past till now)	since 1980
for	over a certain period of time (past till now)	for 2 years
ago	a certain time in the past	2 years ago
before	earlier than a certain point of time	before 2004
to	telling the time	ten to six (5:50)
past	telling the time	ten past six (6:10)
to / till / until	marking the beginning and end of a period of time	from Monday to/till Friday
till / until	in the sense of how long something is going to last	He is on holiday until Friday.
by	in the sense of at the latest up to a certain time	I will be back by 6 o’clock. By 11 o'clock, I had read five pages.

Prepositions of place (position / direction)

English	Usage	Example
in	room, building, street, town, country book, paper etc. car, taxi picture, world	in the kitchen, in London in the book in the car, in a taxi in the picture, in the world
at	meaning next to, by an object for table for events place where you are to do something typical (watch a film, study, work)	at the door, at the station at the table at a concert, at the party at the cinema, at school, at work
on	attached for a place with a river being on a surface for a certain side (left, right) for a floor in a house for public transport for television, radio	the picture on the wall London lies on the Thames. on the table on the left on the first floor on the bus, on a plane on TV, on the radio
by, next to, beside	left or right of somebody or something	Jane is standing by / next to / beside the car.
under	on the ground, lower than (or covered by) something else	the bag is under the table
below	lower than something else but above ground	the fish are below the surface
over	covered by something else meaning more than getting to the other side (also across) overcoming an obstacle	put a jacket over your shirt over 16 years of age walk over the bridge climb over the wall
above	higher than something else, but not directly over it	a path above the lake
across	getting to the other side (also over) getting to the other side	walk across the bridge swim across the lake
through	something with limits on top, bottom and the sides	drive through the tunnel
to	movement to person or building movement to a place or country for bed	go to the cinema go to London / Ireland go to bed
into	enter a room / a building	go into the kitchen / the house
towards	movement in the direction of something (but not directly to it)	go 5 steps towards the house
onto	movement to the top of something	jump onto the table
from	in the sense of where from	a flower from the garden

Other important prepositions

English	Usage	Example
from	who gave it	a present from Jane
of	who/what does it belong to what does it show	a page of the book the picture of a palace
by	who made it	a book by Mark Twain
on	walking or riding on horseback entering a public transport vehicle	on foot, on horseback get on the bus
in	entering a car  / Taxi	get in the car
off	leaving a public transport vehicle	get off the train
out of	leaving a car  / Taxi	get out of the taxi
by	rise or fall of something travelling (other than walking or horseriding)	prices have risen by 10 percent by car, by bus
at	for age	she learned Russian at 45
about	for topics, meaning what about	we were talking about you

(Adapted from: http://www.ego4u.com/en/cram-up/grammar/prepositions; http://www.englishclub.com/vocabulary/prepositions.htm)