In very general terms, prepositions express different kinds of relations between entities. Consider, for example, a common preposition like on, as in the following example:
(1) The books on the table are cheaper.
Here the preposition serves to relate two entities, a number of books and a table. The relation encoded by the preposition is a spatial one; one entity is located on the top surface of the other. It is easy to come up with other similar examples, where this concrete, spatial relation is encoded by on. A great many abstract uses of prepositions, may, in fact, be traced back to a concrete, spatial relation. Consider the following examples, where the prepositions are all used to encode temporal relations which can be derived from spatial ones):
(2) At 11 o’clock
(Time conceived of as a point; the concrete spatial meaning is found in: at his desk, at the bus stop, etc.)
(3) In the morning
(Time conceived of as an area; the concrete spatial meaning is found in: in the garden, in Japan, etc.)
(4) On Friday
(Time conceived of as a surface; the concrete spatial meaning is found in: on the table, on his head)
Other types of extensions of spatial meaning occur in the following examples:
(5) Under the leadership of the professor
(Hierarchical position conceived of as vertical position)
(6) In love
(Emotion conceived of as a container. Note also the phrase fall out of love, with the same metaphorical construal.)
(7) Through many different sources
(Instrument/Source conceived of as the traversal of three-dimensional space; the concrete spatial meaning is found in: through the tunnel)
Even though the use/meaning of prepositions can often be explained, it is much more difficult to predict what preposition is used in a given sense. Thus, the fact that we say on the pavement, rather than *in the pavement, whereas both in the street and on the street are possible (with some dialectal variation) cannot be predicted just based on our conception of spatial relations.
Some verbs are followed by adverb particles. Examples are: put on, take off, give away, bring up, call in.
He was brought up by his grandmother.
Sometimes the particle is detached from the verb and put after the object.
He took his boots off.
They called the doctor in.
John put his hat on.
He threw the apple away.
You must send them back.
Note: that the particle is put after the object when the object is a personal pronoun — it, me, us, them etc. — or when it is comparatively short.
Many words can be used as both adverb particles and prepositions. There is some difference between an adverb particle and a preposition. While the particle is closely tied to its verb to form idiomatic expressions, the preposition is closely tied to the noun or pronoun it modifies.
The following words are used only as particles and never as prepositions — away, back, out, backward, forward, upward, downward.
When the object is long or has to be made prominent or when it is qualified by an adjectival phrase or clause, the particle comes before the object.
The principal gave away the prizes.
He put on an air of innocence.
He brushed aside all the plans I had carefully formulated.
The sailors put out the fire in the hold of the ship.
We should not throw away anything useful.