Ambiguity is the quality that allows more than one interpretation of a story or event to made.

As the story opens, it is a beautiful day, and we have no reason to think the lottery described is anything but a happy event. We learn that:

The morning of June 27th was clear and sunny, with the fresh warmth of a full-summer day; the flowers were blossoming profusely and the grass was richly green. The people of the village began to gather in the square.

It would make perfect sense to imagine a lottery being held perhaps to raise money for a good cause, with the winner possibly winning a washing machine or some other appliance. Children attend, which also cues us to believe this is a friendly, family-oriented event. Why boys would put stones in their pockets is, at this point. ambiguous, but it seems an ordinary thing to do within the context of the scene. In the same way, Bobby Martin's father speaking to him "sharply" to stay with the family doesn't seem ominous at all until we find out the nature of the lottery.

The barbarism that unfolds is all the more shocking given how ordinary and pleasant the opening descriptions are.

While Shirley Jackson does provide very subtle foreshadowing, there is certainly ambiguity in her narrative about the lottery, a function that only takes a short while:

[It] took less than two hours, so it could begin at ten o'clock in the morning and still be through in time to allow the villagers to get home for noon dinner.

Throughout the narrative, a third-person objective point of view is used, and, while details are provided, there are no judgments given, lending ambiguity as to what is to occur. Certainly, Jackson disarms her readers with the bucolic scene of the men of the village talking of "planting and rain, tractors, and taxes." Along with this description, Mr. Summers, "a round-faced, jovial man" who waves and calls out, "Little late today, folks" as though everyone has assembled for a picnic or fair does not appear to be someone who would conduct anything sinister. Most importantly, the word "lottery" is ambiguous of itself, for it is never actually defined, and, thus, the gathering of the villagers seems harmless. 

In Shirley Jackson's "The Lottery," how is the lottery used as a symbol?

As its very title suggests, Shirley Jackson’s short story “The Lottery” focuses on an apparent game of chance.  Unless lotteries are rigged, they are supposed to be decided purely by accident, not by any design.  Jackson uses the basic symbol of lotteries in a variety of ways, including the following:

• Lotteries are usually considered good things in which some people win a great deal and most people lose just a little.  In this lottery, however, one person loses greatly (she is stoned to death), while the community at large apparently thinks that it actually benefits.
• In typical lotteries, the winners are quite happy to have won; Tessie Hutchinson, of course, is anguished to have been chosen.
• Most lotteries allow individuals to choose to participate or not participate. In this lottery, however, there seems no escape clause. Not only are all citizens of the town expected to participate, but they do not even have to be physically present, as is implied in the following passage:

"Well, now," Mr. Summers said soberly, "guess we better get started, get this over with, so's we can go back to work. Anybody ain't here?"
"Dunbar," several people said. "Dunbar, Dunbar."
Mr. Summers consulted his list. "Clyde Dunbar," he said. "That's right. He's broke his leg, hasn't he? Who's drawing for him?"

• Lotteries that do involve the possibility of danger (such as the military draft) do not generally have such happy, cheerful, willing participants as does the lottery described in Jackson’s story. It is this tone of cheerfulness that makes us fail to suspect, until very near the end of the work, that this lottery is anything to fear.
• Lotteries, once begun in one community, tend to spread to others, as can be seen from the multiplication of state lotteries in the U. S. during the past several decades. Once they are established, they tend to endure.  In Jackson’s story, the town the story depicts is one of a decreasing number of communities that still have lotteries.
• Lotteries designed to benefit communities usually do so in quite unambiguous ways, such as funding schools or funding services for the elderly. The lottery depicted in this story, however, seems rooted in mere superstition that maintaining the lottery will ensure a good annual crop of corn.

In many ways, then, Jackson treats lottery symbolism with a good deal of irony in this work.

In "The Lottery," how do foreshadowing and symbolism convey the story's theme?

“The Lottery” is an ironic story in which a community chooses a person by lottery to be killed.  One of the main themes is that people will be cruel if it is acceptable or required that they be so.

A theme of the lottery is “the blind following of tradition and the negative consequences of such an action” (enotes, themes).  The first hint that something is off is when the school-children begin filling their pockets with stones.

Bobby Martin had already stuffed his pockets full of stones, and the other boys soon followed his example, selecting the smoothest and roundest stones. (p. 1, see first link)

The reader should begin to wonder why Bobby is gathering stones, and why the others follow Bobby’s example.

When the adults arrive, it becomes even clearer that something is wrong.  This is not child’s play.

Soon the men began to gather. Surveying their own children, speaking of planting and rain, tractors and taxes. They stood together, away from the pile of stones in the corner, and their jokes were quiet and they smiled rather than laughed. (p. 1)

The men seem uncomfortable, foreshadowing trouble involving the stones.