The best way to start an argumentative essay is to have a strong thesis already in mind.  A thesis will state your point clearly and simply.  Then you can do a clever hook related to your thesis.  One of my favorite ways to start an argumentative essay is to tell a little story or quote a shocking statistic.  For example, if you were writing about school cafeteria food, you might begin with: More than 60% of students at our school do not like the food.

After writing the body of the paper, you should be ready to write the introduction.  The introduction should probably be the last aspect of your paper that you write.  

There are four parts of an introduction to include:

A. the attention getter

•      a good story
•      an authority's opinion
•      an interesting or startling statistic with explanation
•      a personal experience

B. The tie-in to the topic sentences

You should have a couple of sentences that explain the attention getter and its relevance to the topic.  

C. Introduce the topic

Indicate the importance of the topic, its relation to any long-term problem

If needed, a brief definition can be given here.

D. The thesis or argumentative claim

This should be one of the best sentences in the paper.  This is the controlling sentence for the paper. A second sentence can include the aspects of the topic that are going to be discussed.

Altogether the introduction should be about seven -ten sentences.  Of course, the number of sentences does depend on the how long you make your attention getter. 

Grab the reader's attention.  Look for the most interesting way to introduce your topic. 

There are several "How to write an introduction" answers on enotes.  Look for those. Look at this particular url for more information about the introudction.   

http://www.enotes.com/essay/q-and-a/can-you-guide-me-through-how-write-an-introductory-368547

In my opinion, the first thing that you do is to decide what you are going to say in your essay as a whole.  I think that people get too caught up in trying to write a clever introduction when they don't know yet what they are going to say.  Write your body paragraphs first.  Then you will know what you are arguing and you can do what Post #2 says you should do.

When writing an argumentative essay, your thesis statement will always present two things - 1) a topic and 2) your position on that topic. 

For instance, if you are writing about the subject of makeup, your thesis statement will identify a position on this subject:

Due to perceived peer pressure to appear older, young girls begin to wear makeup at inappropriate ages.

There are a variety of ways to open an essay like this one. In your introductory paragraph, you can begin with the thesis statement or begin with context or a rhetorical question/rhetorical statement.

Middle school is place of many firsts, for girls and boys. Braces and broken voices are naturally normal parts of middle school life.