There are many ways to introduce an academic essay or short paper. Most academic writers, however, appear to do one or more of the following in their introductions:

• establish the context, background and/or importance of the topic
• present an issue, problem, or controversy in the field of study
• define the topic and/or key terms used in the paper
• state the purpose of the essay or short paper
• provide an overview of the coverage and/or structure of the writing
• Slightly less complex introductions may simply inform the reader: what the topic is, why it is important, and how the writing is organised. In very short assignments, it is not uncommon for a writer to commence simply by stating the purpose of their writing.

Introductions to research dissertations and theses tend to be relatively short compared to the other sections of the text but quite complex in terms of their functional elements. Some of the more common elements include:

• establishing the context, background and/or importance of the topic
• giving a brief review of the relevant academic literature
• identifying a problem, controversy or a knowledge gap in the field of study
• stating the aim(s) of the research and the research questions or hypotheses
• providing a synopsis of the research design and method(s)
• explaining the significance or value of the study
• defining certain key terms
• providing an overview of the dissertation or report structure

(Source: University of Manchester)

See more about:

Referring to sources
Describing methods
Reporting results
Discussing findings 
Writing conclusions