The most famous essay ever written about Shakespeare's Macbeth is "On the Knocking at the Gate in Macbeth," by Thomas De Quincey, which originally appeared in The London Magazine in 1823. The first paragraph of De Quincey's essay reads as follows:
From my boyish days I had always felt a great perplexity on one point in Macbeth. It was this: the knocking at the gate, which succeeds to the murder of Duncan, produced to my feelings an effect for which I never could account. The effect was, that it reflected back upon the murderer a peculiar awfulness and a depth of solemnity; yet, however obstinately I endeavoured with my understanding to comprehend this, for many years I never could see why it should produce such an effect.
This introduction is useful in several ways. The first sentence shows that De Quincey is taking a personal approach to the subject. The next sentence limits the essay to a single aspect of Shakespeare's play, the effect produced by the knocking at the gate which begins in Act 2, Scene 2 and continues into Scene 3 of the play. De Quincey introduces a touch of drama by indicating that he is trying to understand a problem which he has set for himself. The reader will be curious to know whether he succeeded in solving that problem and what the solution was.
The main value in reading De Quincey's essay as a model is in observing that he is not by any means trying to cover the whole of Macbeth but is only dealing with a single facet of a very complex work. This is something you should do yourself. You need to decide on some limited aspect of the play on which you can focus your full attention. Naturally your introduction needs to describe what that aspect is, and it would be very helpful in making your essay interesting if you presented it, as De Quincey does his, as a question or a problem for which you are trying to find the answer. In other words, it is a good idea to suggest in your introduction that you are going to try to solve a problem or a puzzle. You can take a personal approach, as De Quincey does, if you wish. Or you can leave yourself out of it and write entirely in the third person.
There are many questions and problems in the play. You don't even have to search your own brain for them, because the "Homework Help" section in the eNotes voluminous coverage of Shakespeare's play contains 4750 entries which are mostly questions about it. For example:
In Macbeth, why doesn't Lady Macbeth trust Macbeth to carry out the plot against the king?
Here's a question that has been asked many times:
Why does Macbeth bring the two daggers back to his and his wife's bed chamber when he was supposed to leave them near Duncan's body?
You should pick any question or problem or issue that intrigues you, but it seems prudent to pick one for which you think you know the answer. You don't need to do a lot of research, since you are not required to write a research paper. You can express your own opinions and also refer to what others have written about the same subject. Some of the reference links below should be helpful to you.
Don't start work by trying to write your introduction. Start work by trying to find a single aspect of Macbeth that you want to deal with in your essay.