Think of your paper in terms of the social transaction with your reader that it actually is. Consider your reader's entry into your paper as if you were meeting them at the door of your house. The analogy is not inappropriate. Consider science-fiction writer Ursula Le Guin's comment:
First sentences are doors to worlds.
What readers need as they leave their own world to enter this new one is orientation. Thus the symbol for the first paragraph is an inverted triangle. What this part of the diagram signifies is that you should begin with general context and then funnel down to the main point which usually comes at the end of the introduction. In this final position you are poised and pointing into the body of the discussion (if, on the other hand, you have a multi-paragraph introduction, your main point or thesis will likely come at or near the end of the section).
Here's a sample introductory paragraph. It was written in a first-year English class by former Guilford student Tripp Oakley.
Feelings of isolation and loneliness pervade the human experience. These emotions cause each of us to search for meaning and finally truth. To fill this spiritual void some of us place faith in a God or emphatically reject the notion of a God just so we can gain some sense of independence. Essentially it is a desperate attempt to escape the fear we feel towards our existence. Flannery O'Connor felt this struggle which is exemplified by her character, the Misfit, in her short story, "A Good Man is Hard to Find." Through the Misfit's views on a world void of faith and his struggle with unwarranted punishment, O'Connor creates the classic existentialist hero.
Note how Tripp begins with general statements to which we can all relate. He is also staking out a particular thematic area. Once he has done this, orienting us to the world of the paper, he downshifts to his specific subject--O'Connor's story--and then establishes a claim, or thesis, which his paper will then go on to prove. We can assume that in the paragraphs that follow, Tripp will demonstrate systematically that the Misfit embodies the traits of the existentialist hero.
Another way of approaching the first sentence or sentences is as a "hook" which captures the reader's attention. In journalism, we would call this the "lead."
There are many strategies for opening a paper. These include, according to the Harbrace College Handbook, an interesting fact or unusual detail, an arresting statement, an anecdote, a question which the paper will answer, an appropriate quotation, an illustration, general information as background. Whatever you choose, think of your reader's needs and what's most appropriate given your subject.