As an English and Composition teacher, I will offer you the same advice I give to my own writing students. Please consider something first: not all teachers appreciate the same things in writing. 

To begin, it is always important to have a strong idea of what the focus of the essay will be. Your general topic (the broad subject the teacher has assigned) must be limited and focused. For example, the broad subject of "Media" needs to be greatly limited. The topic of "Media" is far too general to construct a focused essay around. 

In order to define where one may go with the topic "Media," do a prewrite. You can freewrite, map (cluster), or brainstorm all things which relate to "media." Once finished with a prewrite, examine the prewriting material. What does it lead to? What are the main points? Is any of the material similar? Once you can answer these questions, a more direct plan of action can be defined. 

Let us stay with the topic of "Media." Pretend that the prewrite material focused upon the negative aspects of media upon teenagers. This raw material needs to be focused further. How is it negative? What aspects are negative? What specific aspects are negative? You could conduct another brainstorming or map to come up with supporting information and a general thesis. 

Let us say that the second round of writing, for supportive material, allows you to focus upon the detrimental aspects of photo-shopping models on the self image of teenage girls. This would be what you would focus your thesis on. 

Now, onto the introduction paragraph. You first need to grab your reader's attention. While some teachers may differ on how to do this, the most popular ways to do this are to use statistics, anecdotes, and quotes. This attention getter will be the first sentence on the introduction paragraph. The thesis will be your final one to two sentences in the introduction paragraph. Bridging the attention getter and thesis should be information which will lead your reader through your thought process behind the paper. It is here where you should illustrate, not prove or support, the point the essay will make. 

Essentially, you should insure that you have a focused thesis, a way to grab the attention of your reader, and a point to make in an introduction to an essay. 

What are effective ways to begin an essay?

The introductory paragraph of an essay establishes the tone and voice of the writer and lays out what is called the "blueprint" of the essay. Especially if the essay is for a class assignment or the answer to an essay question, the outline of the five-paragraph essay as explained in The Practical Writer is a valuable guide. According to authors Edward P. Bailey and Philip A. Powell, the introduction should have three parts:

1. a motivator
2. a thesis statement
3. a blueprint

The "motivator" begins the essay and is all but the last sentence of the introductory paragraph. As the name suggests, the purpose of this motivator is to hook the readers' interest and curiosity, thus motivating them to read the essay. The last sentence of the introduction is the thesis, with the "blueprint" which gives what will be the topic sentences of each paragraph of the essay; i.e. the three opinions that relate to the thesis and will substantiate it. An introductory paragraph is brief--4 or 5 sentences.

Motivators can be the following:

1. a personal observation that relates to the topic, leading to its relevance to the topic by means of an explanation in general terms of the topic
2. a pertinent citation from the work that is to be analyzed or discussed in the essay, along with authorial comments relevant to the topic
3. an anecdote that is humorous or thought-provoking that also relates to the thesis with a short explanation
4. a question followed by some thought-provoking ideas relevant to the thesis