Prepositions are words used in a phrase to explain the relationship between words in a sentence. The preposition (for example, to) links the rest of the words in the phrase (for example the store) to other ideas within a sentence. This link clarifies relationships such as time, location, or direction (as in “Garfield went to the store”).

Prepositions in Sentences

Let’s look at how a preposition functions in a sentence.
Ex. Viewers smiled during the ceremony.
 
In this sentence, during is a preposition. It relates smiled to ceremony by defining the time at which the smiles occurred. During the ceremony is the prepositional phrase.

The object of a preposition is a noun or pronoun; in the example above ceremony is the object of the preposition during. There may also be modifying words between the preposition and its object: after the heavy rain, before the morning meeting, behind the big, angry dog. (Note that the subject of a sentence is never in a prepositional phrase.)

There are many prepositions in English; in fact, they’re some of our most commonly used words. You can think of many prepositions when imagining a lake: you can go around, through, across, over, under, in, into, from, past, to, on, or toward a lake. You could also be above, beside, behind, beyond, and near the lake.  Learning which prepositions are preferred in certain contexts can be confusing. While there are some general guidelines to follow, many just have to be memorized.

Time

We use prepositions to discuss time in hours, days, months, and years. The most common prepositions of time are in, on, and at.
In:  Periods of time—years, months, weeks, and general times of day—can be thought of as spaces of time in which one can reside, so use in.
Ex. Sales peaked in 2009.
Ex. John plants tomatoes in January.
Ex. Her baby is due in three weeks.
Ex. Some people enjoy naps in the afternoon.
 
On:  We use on to describe days of the week or specific dates.
Ex. Is your birthday on Monday?
Ex. On December 21, 2012, the Mayan calendar ends.
 
At:  Specific times can be thought of as points of time, so use at.
Ex. The child had an appointment with a doctor at 7:00 a.m.

Location and Direction

Prepositions can indicate the exact location of a noun in space. The prepositions on, at, and in, for example, describe specific locations.
Ex. The student stood on the statue in Academic Plaza at Texas A&M University.
 
Prepositions can also indicate the direction in which something is moving through space.
Ex. The elephant moved across the lake.

Prepositions That Take Verbs

Some prepositions are typically combined with certain verbs, adjectives, or nouns.

agree with	I agree with the man who is speaking.
blame . . . on	Don’t blame your problems on me!
consist of	The solution consists of some strange chemicals.
depend on/upon	Do not depend upon other people.
insist on	The decorator insists on blue drapes.
listen to	Listen to me when I’m speaking to you.
look at	It is not polite to look at someone for a long time.
remind . . . of	You remind me of a bear.

The University of Ottawa has some further reading on prepositions.

References

MacFayden, Heather. “What is a Preposition?” University of Ottawa Writing Centre. 2007. Web. 16 Feb. 2010.
Tickle, Amy. The Writing Process: A Guide for ESL Students. New York: HarperCollins College Publishers, 1996.
“Verbs That Take Prepositions.” Akkor, Sedef, ed. Undergraduate Writing Center. University of Texas at Austin. 2006. Web Document. 16 Feb. 2010.
Vered, Lily. “An Activity for Teaching Prepositions Associated with Time.” The Internet TESL Journal 4 (1998): n. pag. Web. 5 Feb. 2010.