A preposition describes a relationship between other words in a sentence. Prepositions are “locators”, in other words, they explain when and where something is happening. Those are the two questions to ask concerning preopositions: When? Where? Here is an example: The student sat behind the desk. The preposition is the word “behind.” Where was he sitting? Behind. The other question to ask is the when question. Prepositions also describe when something is happening. Here is an example: My class starts in the morning. The “when” preposition is the word morning

The following is a qoute from Garner's Modern American Usage, Oxford University Press, 2003.

“The spurious rule about not ending sentences with prepositions is a remnant of Latin grammar, in which a preposition was the one word that a writer could not end a sentence with. But Latin grammar should never straightjacket English grammar. If the superstition is a “rule” at all, it is a rule of rhetoric and not of grammar, the idea being to end sentences with strong words that drive a point home. That principle is sound, of course, but not to the extent of meriting lockstep adherence or flouting established idiom.”

The preposition of expresses origin or location.
She always dreamed of being a movie star.
This is a picture of my parents

The preposition from expresses origin or location.
He is from Chicago.
This letter was sent from my mother.

Go here to see more examples of “of” and “from”

The preposition of is used to create a sense of belonging to, relating to, or being connected with something.

I have concluded that secret of the slot machines is that you can't ever win.
The best part of the movie is at the end.
The first page of the book gives the publishers information.
I have always dreamed of one day being rich and famous.

Used to indicate reference:

I got married in the summer of 1997.
This is a picture of my wife.
I got a discount of 10 percent using my military ID.

Used to indicate an amount or number:

I drank one cup of coffee this morning.
A large number of students gathered for the lecture.
I try to get at least eight hours of sleep every night.
I earned a perfect score of 100 on my last exam.

Many authors and writers start some of their sentences with prepositions and it works very well for them. You simply have to be careful when starting a sentence with a prepostion, that the sentence does not become fragmented as a reuslt.

Here is an example with the preposition up.
Correct usage: We ran up the mountain.
Incorrect: Up the mountain we ran.

Here is an example with the preposition over.
Correct: The rabbit jumped over the log.
incorrect: Over the log the rabbit jumped.

Here is an example with the preposition aboard.
Correct: We got aboard the train to ride down to San Diego.
Incorrect: Aboard the train we got to ride down to San Diego.

Here are some good examples of sentences starting with prepositions:
In case of fire, do not use the elevators.
After football, we go out for pizza.
Over spring break, I went to visit my Grandmother.

Remember that prepositions are connecting words and are generally used to connect a noun or pronoun to another word in a sentence. You can indeed start a sentence with a preposition, just be sure you use it correctly.

The preposistion against can actually convey several different types of meanings. I'll demonstrate: Against can be used as a location preposition, or a direction preposition, or as an abstract preposition. Here are some examples:

In the sentences below, against is being used to show the location of an object.

The brown shelf against the wall is full of books.
Sam climbed the ladder that was against building.
All the cabinets stacked against the wall are empty.

In the sentences below, against is being used to show the location of an action.

He banged his fist in frustration against the wall.
The strong wind blew the rain against the window.
The remains of the broken ladder were leaning against the building.

In the sentences below, against is being used to convey the direction of movement.

The seagull wearily flapped his wings as he flew against the wind.
It can be very difficult to move against the flow in a crowd of people.
I had to swim against the current in the last leg of the race.

In the sentences below, against is being used to convey an abstract sense of opposition.

Our team played against the the toughest team in the state and won!
If you had to, could you defend yourself against an attack?
I am against the new law that Congress passed last month.

Some prepositions are used for logical relationships. Logical prepositions include of / out of / from / for / on / by / without. There are many more. Logical prepositions show the relationship between a part, or parts, and the whole. Let me demonstarte this for you.
John is a citizen of Australia. The preposition of shows the logical relationship John has with Australia.
Here is another example.
Jane is going to the store for ice cream. The preposition for shows the logical relationship between Jane and the store.

This is a good question which comes up often. In American English you would use the preposition on. In England you would you use the preposition in. Both are correct since both prepositions can used to indicate place. My personal preference is to use on in this instance.