Choose the direction of your essay. Infanticide has been observed throughout human history, including the modern day, as well as in other animals. An all encompassing essay on infanticide would likely be too broad, thus it is best to narrow your topic by considering what subsection of infanticide best fits your essay.
Research information applicable to your essay. Some countries, such as the United States, keep detailed statistics on infanticide, while others records may be less specific.
Consider your audience. An essay on infanticide can easily lead to an emotional appeal to help save infants from murder. Be sure that the tone of your essay is appropriate for the audience; an emotional appeal may make sense in a newspaper editorial, but is less applicable if it is an academic paper on infanticide in ancient Greece.
Draft an outline. Be sure you structure your essay in a logical manner: even if it is emotionally based, you want to buttress your argument with facts. If it is more academic in nature, be sure that your thesis statement is clear.
Write a strong introduction that has a clear thesis statement. For example, if you're going to write an emotional appeal and try to get help for the countries that have a high rate of infanticide, you might want to lead off with the devastating image of a family willfully murdering a child in order to grab your audience's emotions.
Construct your body paragraphs based on the information that you found while researching. This is especially pertinent for the non-emotional appeal arguments (such as looking at infanticide in the animal kingdom or throughout history); each relevant sub-section or statistic should ideally get a paragraph of its own in which the information is stated and analyzed (e.g. state that lions sometimes kill their infants and then explain why).
End with a concluding paragraph that re-summarizes the thesis and, if necessary, re-states any emotional appeal. Do not use the conclusion to introduce new statistics or information, but instead just summarize your overall argument.