it written in the third person, with words like "they"? And how much does the narrator know?

In this case, the story is being written in the third person. We can see that the narrative voice does not use "I" statements; it isn't telling us about events which the narrator seems to have personally had a part in. On the contrary, the narrative voice seems to replicate that of a documentary, particularly given that it begins very exactly with the date "June 27th."

Note the use of the distancing term "the villagers" to describe the people in the story. This is a strong indication that the narrator is not one of these people. However, at the same time, the narrator is aware of what the villagers think and feel, albeit in broad strokes, rather than individually. The narrative voice knows where the box is put over the course of the year, and knows how the villagers feel not only about the box and the tradition, but also about the other villagers.

This general air of knowing everything about everyone in a narrative voice is normally described as omniscient narrating, or all-seeing narration. The narrative voice of this story, then, is third-person omniscient.

The point of view employed by "The Lottery" is third-person omniscient. At first, the narrator only describes what is immediately observable: that people are gathering together, that the men smile rather than laugh, that the women call out to their children. A third-person objective narrator cannot report any characters' thoughts and feelings, and a limited omniscient narrator can report only one character's thoughts and feelings.

However, the narrator soon begins to describe the thoughts and feelings of multiple characters, something only an omniscient narrator can do. First, the narrator describes Mr. Summers as a "jovial man" who has "time and energy to devote to civic activities." These are not immediately observable and require some intimate knowledge of his thoughts and feelings in order to ascertain. Further, "people were sorry for him, because he had no children and his wife was a scold." The statement that people feel sympathetically toward Mr. Summers is a description of how they think, not something they say aloud during the course of the story.

Moreover, the narrator tells us that "no one [in the village] liked to upset even as much tradition as was represented by the black box" used in the lottery. Again, this is not dialogue but, rather, a description of the villagers' internal thoughts and feelings. It is information like this that helps us to ascertain that the third-person narrator is omniscient rather than objective (not reporting anyone's thoughts and feelings) or limited omniscient (only reporting one character's thoughts and feelings).

The point of view of "The Lottery" is the third person point of view.

A third person point of view places the narrator outside of the events happening in the story.  The narrator obviously knows characters and things that are happening, but a third person narrator means that the story's narrator is not a character within the story.  More specifically, the narrator of "The Lottery" is narrating from the third person objective point of view.  This allows the narrator to jump from person to person and group to group.  Readers are allowed to listen in on various conversations as if we are eavesdropping on everybody.  

The fact that the narrator is only capable of eavesdropping on people is why this story's point of view is third person objective and not third person omniscient.  An omniscient narrator is privy to the internal thoughts of characters, and the narrator of "The Lottery" never indicates that knowledge. That's a good thing for this story too.  If readers knew the thoughts of the characters, the final shocking moments of the story wouldn't be as shocking.  

One natural effect of the third person narration is that readers feel a bit of distance from the events happening in the story.  We feel invested to a certain extent, but we also know that the events (good or bad) are always happening to somebody else.  That distance is important for this story.  While readers are appalled at the realistic feel of the lottery, we can at least take comfort that the people are not our personal friends.  It's not my town's tradition.  It's their town's tradition.  I've often wondered what this story might be like from the first person perspective.  I don't think the ending would be as shocking, because a character narrator would likely give away his/her apprehension about the lottery system.  

In their excellent book, Points of View: An Anthology of Short Stories (Rev. ed. 1995), editors James Moffett and Kenneth R. McElheny have arranged forty-four short stories according to points of view, proceeding from the most subjective up to the most objective. They classify Shirley Jackson's "The Lottery" as ANONYMOUS NARRATION--NO CHARACTER POINT OF VIEW, which is the editors' most objective category. In their introduction to this class of stories they write:

By staying outside the minds of all the characters, a narrator drops the role of confidant and relies entirely on eyewitness and chorus knowledge alone. Stories of this sort that emphasize the eyewitness role tend toward scripts that include virtually nothing a bystander would not see and hear...

The narrator of Jackson's "The Lottery" is anonymous, but not omniscient like many of the anonymous narrators of short stories, such as Jack London's "To Build a Fire," to take only one example, or Anton Chekhov's story "The Bet," both of which, incidentally, would fit into Moffett's and McElheny's category of ANONYMOUS NARRATION--SINGLE CHARACTER POINT OF VIEW. The reader of "The Lottery" is placed in the position of an observer, or "eyewitness," and only knows what he sees and hears. This is an effective way for Jackson to present this particular story because it enables her to keep the reader in the dark and in growing suspense. The reader has a sense that something pretty awful is going to happen, but doesn't find out until close to the end what it is. The effect of the story would be ruined if the reader could see into some of the characters' minds and learn what this annual ritual was supposedly all about. We only get hints from some of the characters, such as Old Man Warner. When Mr. Adams tells him that they are thinking of giving up their lottery in a nearby village, 

Old Man Warner snorted. "Pack of crazy fools," he said. "Listening to the young folks, nothing's good enough for them. Next thing you know, they'll be wanting to go back to living in caves, nobody work any more, live that way for a while. Used to be a saying about 'Lottery in June, corn be heavy soon.'"

We get the impression that this lottery must have started out a long time ago as a human sacrifice to some god or goddess of agriculture. Any knowledge we pick up has to be with our own eyes and ears. We never really do understand why these seemingly ordinary, kindly, neighborly people continue to participate in this hideous, superstitious ritual year after year--but that is precisely the author's intention. 

"The Lottery" is told in the past tense, from a third-person omniscient point of view. This means that the narrator is not a participant in the story's action and does not use the first-person pronoun "I," but the narrator does know and can report on the thoughts and feelings of any and all characters.

For example, when Mr. Summers is first introduced, the narrator says that "people were sorry for him because he had no children and his wife was a scold" (my emphasis). Thus, we see that the narrator knows what the townspeople think. The narrator also says that "so much of the ritual had been forgotten" that Mr. Summers was able to convince folks to replace wood chips with slips of paper in the lottery (my emphasis).

Further, the narrator outlines other traditions that have faded, such as the fact that "now it was felt necessary only for the official to speak to each person approaching" rather than using the traditional ritual salute, etc. (my emphasis). In addition, the narrator knows that "Mr. Summers and every else in the village knew [...] perfectly well" that Mrs. Dunbar did not have a grown son to draw for her family (my emphasis). I hope these examples show how the narrator knows the thoughts and feelings of the characters, making the narrator an omniscient (all-knowing) one.

The key element of narration in Jackson's "The Lottery" is that it does not give character thoughts.  This is the essential element of Jackson's narrator.

The narrator is detached and uninvolved, objective.  The narration is limited to history, description, dialogue, and action.  What the narration does not include is the omniscient ability to read characters' minds.  No thoughts are revealed.  This is the key to the surprise ending.  The objective narration does not give away what the lottery is really about.  The surprise ending would be impossible if the narrator were omniscient.  Reading character thoughts would give away what they are really doing there, and what the lottery is really about.

As the enotes Study Guide to the short story reads:

Jackson's narrative technique, the way she recounts the events in the story, is often described as detached and objective. Told from a third-person point of view, the narrator is not a participant in the story. The objective tone of the narrative, meaning the story is told without excessive emotionalism or description, helps to impart the ordinariness of the barbaric act.

The narrator can't be a part of the story, and can't reveal character thoughts.  To do either would destroy the surprise ending.

The point of view is third person objective, omniscient, and detached. It is the only logical point of view for this story because the character is present, knows everything, but emits no opinion, emotion, nor personal dislike or like towards the situation.

It is also the only logical point of view for the story because the narrator is meant to be a part of the story as a witness, and so shares the pathos of the community: That it is numbed to death, and to the atrocious practice of the lottery.

Finally, the shock does not come from the narrator but from the reader, precisely because of how detached the narrator is, and how openly bluntly the end is presented. That is the purpose of the point of view in its entirety.

The story of "The Lottery" describes the annual ritual in this unnamed town, where the townspeople gather to select a name from the box offered up by Mr. Summers.  It appears that this exercise has been occurring for a long time.  Everyone is included, even the children: no one is exempt.

As with Shirley Jackson's "The Possibility of Evil," the evil prevalent in the story is not obvious at first.

The story is told in third person omniscient.  The author describes the situation not as if he/she were a part of the business, but a casual observer on the outside, looking in.  The mood of the author's writing does not convey what is about to take place, another hallmark of Jackson's writing.  It simply describes what is taking place, and it is not until Tessie Hutchinson realizes her family has been chosen that the anxiety in her demeanor convey a sense of suspense and dread.

What is even more disturbing (in retrospect) is that when their family's name is called, she suggests that other members of her family not living in their house also be included in the final drawing.  Equally disturbing is the rejoicing of her children when they don't pick the paper with the black mark, her husband's stoicism when he realizes that he has not been chosen, and finally, the town's calm acceptance of what is to come as they pick up the stones with which they will kill Tessie by stoning her to death.

Well, strictly speaking, "The Lottery" is written using the omniscient point of view. It is not written using the first person point of view, and whilst it is written using the third person, it does not follow the action from the perspective of one character. The issue, however, is that Jackson as the omniscient narrator chooses to restrict the amount of information that we are given. Of course the characters all know what is going on, but crucially we as readers do not, and it is only in the final paragraphs that we understand what this Lottery is all about and what the tragic conclusion of it is. For Jackson to have given us access into the minds of the characters would have destroyed this massive sense of shock that we are provided with and made all the subtle elements of foreshadowing that she gives us (like the boys collecting stones at the beginning) unnecessary.

After an introductory paragraph of omniscient narration, the point of view shifts to be largely that of the villagers themselves. We know this because the first sentence of the second paragraph ends with the words "of course:"

The children assembled first, of course.

The "of course" indicates insider knowledge: we are learning about this odd ritual from people who are so completely familiar with it is assumed everyone knows the unwritten protocols.

We could imagine, if this story were filmed, the "videocamera" of the first paragraph filming from a distance, perhaps with a voice-over. For the second paragraph and onward, the camera would have zoomed in to be among the crowd, up close and personal.

The fact that we are experiencing the story from the point-of-view of insiders means that we only share their fragmented incomplete knowledge and understanding of this ritual. It is so ordinary that they wouldn't think to stand back and research it or try to understand it in a more global way. It just is what it is.

Being closer to the characters also raises the emotional intensity of the story. We may not know all the facts of how this ritual evolved, but we feel the fear it evokes.

In a story told with an objective point of view, the narrator does not focus on one character.  It contributes to the theme that no one in the story is responsible.  This allows for the full force of the story to be felt when the reader realizes that the people are randomly killing one person a year. 

The narrator of a story influences how a story is told.  If a story has an objective narrator, the narrator does not influence the reader’s opinion, because the narrator does not give an opinion.  The reader has no idea what is coming, and there are only subtle hints that something is wrong.

The lottery was conducted--as were the square dances, the teen club, the Halloween program--by Mr. Summers, who had time and energy to devote to civic activities. (p. 1)

There is no commentary on Mr. Summers, he simply is involved because he has time.  We do not know how he feels about it, or how the other villagers feel.  We know how no one feels, so we do not realize what is happening.

This does not mean that we do not know what people are thinking at all.  Consider the following passage.

Mr. Graves opened the slip of paper and there was a general sigh through the crowd as he held it up and everyone could see that it was blank. Nancy and Bill. Jr. opened theirs at the same time, and both beamed and laughed, turning around to the crowd and holding their slips of paper above their heads. (p. 6)

In this passage, we learn how people feel in general, and how Nancy and Bill feel.  We are not inside any one person’s head though, so we still really don’t know what is going on yet.