An introduction is what will help guide and direct your writing throughout your essay, so it is very important that you get it right. However, what a 'right' introduction is can be hard to pin down, as it changes depending on your topic.
In general, you use the introduction to specify what you are going to be writing about, how you are going to show your argument, and you can also specify why you have chosen to write on this subject in particular.
For example, if your essay is on King Lear and the question asks you how the play can show us insight into the human psyche, a potential argument can be that the play shows us the internal struggle of multiple characters through the use of setting/lighting/language. In this case, stage directions and soliloquies are important aspects to consider, so in your introduction, you may write something like this:
'I'm going to use Shakespeare's stage directions to show how they are integral to the psychological aspect of the play, as well as how language functions in relation to the behaviour of the characters on stage.'
Once you have your main argument and you know how to defend it, you can go on to begin the main part of the essay.