What is the introduction part of the critical analysis essay?i have to do a critical analysis essay on "the Lottery". I have been asked to do...

Definitely, the introduction is the first paragraph for
your critical analysis essay.  Now, we need to focus on what introductions need
generally and what an introduction to a critical analysis
needs. 

An introduction needs to ease the reader into the
main idea you want to discuss.  Starting with the main point you want to make is not
necessarily a good idea because there is no buildup.  For example, if you were to walk
up to a stranger on the street and say, "'The Lottery' is a story about a people who
blindly follow the leader,"  that stranger would probably walk away from you. You need
to build up to that idea.  Writing an introduction for your audience in no different. 
What would you say first if you wanted to talk about one main idea in this story?  If
your main idea were about people not wanting to take a stand, you might begin with the
idea that there are cowards in every society.  Do you see how that is a general comment,
but it opens the door to the main idea? 

In most
introductions, you want to structure the paragraph so that you keep leading to that main
idea, which is called a thesis statement.  The thesis statement is usually the last
sentence in the introduction, and we will talk a bit more about that
below. 

In most introductions, you will want to avoid using
any quotes from the story, saving quotes to support your idea in the body paragraphs
that will follow.  It is always best to use your own words in the introduction to
introduce your ideas. 

In a critical analysis, it is
important that you name the story and the author of the story.  Otherwise, no one will
know what you are writing about.  Sometimes, the introduction will include a very brief
synopsis of the story, including a sentence or two about the characters, the setting,
and the plot.  Sometimes this is in the second paragraph, or the story is told through
all the body paragraphs, as you explain the ideas you
have. 

Now, in a critical analysis, the thesis statement,
the statement of your main idea, needs to say something important about the story, for
example, what its theme is, why the setting is important, or an idea about the
relationship between the characters.  A good thesis statement will also give the reader
a "preview" of the points you want to make in support of that statement.  For example,
if I were writing an essay about The Secret Life of Bees, I might
say something like, "'The Secret Life of Bees makes use of many
symbols, the most important ones being water, bees, and a statue of Mary." Now, I don't
know if this is a book you have read, but those are very important symbols in the story,
and now that I have told my reader that these are important symbols, I can set up the
rest of my paper to talk about those symbols, one for each body paragraph.  So, you can
see why the main idea you have must be in the introduction and why you need to give the
reader that preview. 

Once you have all of these elements
in your introduction, you have a great guide to write the rest of the paper.  This is
such an interesting story, and there are many ideas that you can explore to write about
it.