The student's question -- what are some major examples of exposition in Fiddler on the Roof -- does not specify to which format the question is directed: play or film. For the purposes of this discussion, the distinction is non-existent, as both formats employ a first-person narrator in the character of Tevye, the poor dairyman at the center of the story. For purposes of clarity, however, direct quotes cited are from the filmed version of the play.

Exposition, of course, refers to the manner in which the writer and/or director provides background and context for the action depicted before the audience. Classic examples of exposition in films include the Star Wars films, the openings of which provide, in written form, background intended to inform the viewer of the broad context of the story to follow, and the protracted flashback sequence in Casablanca to illuminate the history between Rick and Ilsa so that the viewer can better sympathize with the main protagonist's attitude towards his former lover and the dilemma into which he is cast. In Fiddler on the Roof, the exposition, as noted above, is provided entirely in the form of Tevye's one-sided conversations with God, and in his practice of directly addressing the audience, a method known as "breaking the fourth wall" the separates the audience from the production. The latter tactic, in particular, occurs throughout the play and the film beginning with the opening scene, in which Tevye sets the stage by addressing the audience:

"A fiddler on the roof. Sounds crazy, no? But here, in our little village of Anaetevka, you might say every one of us is a fiddler on the roof trying to scratch out a pleasant, simple tune without breaking his neck. . .You may ask, 'Why do we stay up there if it's so dangerous?' Well, we stay because Anatevka is our home."

In this opening scene, Tevye explains the significance of the film's title, as well as establishes the social context in which the story to follow occurs.

An example of the narrator/protagonist addressing God as a form of expository story-telling, as when Tevye, in exasperation at the continuing persecution of Russia's Jews, looks to the heavens and says, "I know, I know. We are Your chosen people. But once in a while, can't You choose someone else?"

These are two examples of exposition in Fiddler on the Roof. Playwright Joseph Stein's adaptation of the collected writings of Sholem Aleichem is filled with such examples, some in form of song (and, this is, of course, a musical), as when Tevye sings of the pleasures that he would derive from the sudden accumulation of wealth ("If I were a rich man").

The exposition for Fiddler on the Roof is through the musical sequence "Tradition." During this company number, the main character Tevye introduces the major characters and jobs of the townspeople in Anatevka. The song begins with Tevye talking to the audience directly. In introducing his town, he also introduces the foundation of the community - tradition. His opening monologue, spoken while the orchestra plays the opening theme, introduces the traditional Jewish clothing (the fact that they constantly wear prayer shawls to show their devotion to God). In the next few lines, Tevye's personality, religious knowledge, and most importantly, his sense of humor is revealed:

"You may ask, how did this tradition start? I'll tell you - I don't know. But it's a tradition... Because of our traditions, everyone knows who he is and what God expects him to do."

This leads to the introduction of the family: 

The Father: 

Who, day and night, must scramble for a living,
Feed a wife and children, say his daily prayers?
And who has the right, as master of the house,
To have the final word at home.

The Mother: 

Who must know the way to make a proper home,
A quiet home, a kosher home?
Who must raise the family and run the home,
So Papa's free to read the holy books?

The Sons: 

At three, I started Hebrew school. At ten, I learned a trade.
I hear they've picked a bride for me. I hope she's pretty.

The Daughters: 

And who does Mama teach to mend and tend and fix,
Preparing me to marry whoever Papa picks?

Ironically, throughout the play each of these definitions are proven false, much to Tevye's consternation.  This section of Tradition not only defines the responsibilities of each family member, but also indicates the basic principles of religion is the center of Jewish daily life.  Examples of this are the mention of the father reading the Torah, the son's being expected to attend Hebrew School, the mother making a Kosher home, and the ultimate patriarchal paternal control of the daughter's marriage.  

One of Fiddler on the Roof's major themes is about the changes happening to the Jewish culture at the beginning of the twentieth century and how the traditions must adapt to the changing times.  The fact that these roles become fractured during the course of the play symbolizes the much larger changes that will happen to the Jewish community when they are forced from their homes, towns, and countries.   

As the song continues, Tevye enters the town social structure and begins introducing the various key characters in the community such as, Yenta the matchmaker, Nahum the beggar, and the Rabbi.  Each of these introductions has their own comic vignette.  Each introduces the personality of the character and the social customs of the community.  Yenta offers a match of an almost blind girl to a man who is homely.  Nahum chastises a man who did not make money in his shop for not giving his customary donation to the poor.  And, the Rabbi offers a somewhat selfish blessing on the Tsar.    

Tevye then makes the broad statement that the community is a Utopian society where all members get along.  Again introducing Tevye's personality traits he reminds the community of the one fight they had over the sale of a horse.  The community erupts into a fight over whether the deal was good or bad.  The fight grows with every member taking a side, until finally the town erupts with a chorus of "Tradition!"  As they sing the two lines, they fall once more into a unified group, symbolizing the importance of tradition in keeping the community together.  

The song tradition expertly provides the exposition to Fiddler on the Roof.  By the end of the song, the audience is fully aware of the social customs, leaders, major characters, and most importantly, the importance of tradition.  As Tevye says,

"Without our traditions, our lives would be as shaky as... a fiddler on the roof!"

With this knowledge, the audience will understand how Tevye is tormented by the fact that his daughters are one by one breaking the traditions that Tevye holds dear.  Add to this Tsar Nicholas slowly unraveling his outside world, threatening the town, Tevye comes to a crisis of faith.  In the end it is the love between Tevye and his wife, Goldie, that keeps their world from fracturing apart and gives them the strength to move on to a new world.