Think before you write. Are you trying to answer a specific question or prove a specific point? Think through the broad question that has been proposed to you, and make notes of specific aspects of the answers to the question that you will come back to during the term paper.
Define your hypothesis or problem. Make sure you fully understand the point you are trying to make in the term paper. Too often, term papers start with a thesis statement giving the points the paper will attempt to prove and then end up being about something else entirely. Decide how broad or narrow your general approach to your subject matter will be. You might want to start from a broad topic and then give specific narrower applications, or you might want to start with the examples and reach a broad conclusion. If you are attempting to solve a problem in the term paper, begin with a clear explanation of what the problem is and why its solution matters.
Find an attention-grabbing opening. Not all term papers start with dry, logical opening sentences. Consider starting with a pithy and appropriate anecdote or example instead. Pose a puzzle or open with a question that provokes the reader to wonder what the answer might be. Find a great quote that cuts to the heart of your question.
Avoid opening your term paper with a restatement of the question or topic you were originally provided. Since your teacher is likely to be reading many term papers on the same topic, by avoiding this restatement, you will keep your term paper from sounding like everyone else's. Also avoid beginning your term paper by defining terms to be discussed or by using vague and broad statements that don't really mean anything.
Write your term paper introduction with style. Not only do you need a great opening sentence that grabs your reader's interest, you need to write the rest of the introduction well. Make sure all your sentences are clear, that you have omitted needless words and that each sentences actually says something pertinent to the topic at hand. It should go without saying that you also need to make sure your introduction is free of spelling, typographical grammar or punctuation errors.
Consider writing your introduction last. While it seems natural to write the introduction first, since it comes at the beginning of the paper; in reality, you are least prepared to write the introduction at that time. Perhaps the process of actually writing the term paper will help you distill your thoughts, so that you understand your topic and conclusion much better when you are finished. If you write your introduction first, you will almost certainly have to go back and rewrite it significantly to reflect changes you have made and subtopics you have explored in the writing of the term paper. Instead, leave the introduction until last, and write it when you are fully prepared to introduce the topic at hand.