This is a very broad topic, and while that lends the benefit of a large amount of material to work with, it also makes it possible to become too detailed or nuanced, and miss the big picture.
Some important points are;
- How are you defining hope and despair? Explain your definition in the essay so that it's clear to the reader why certain things would be classified as they are. For example, when the witches prophecy Macbeth's ascendance to the throne, would this be considered a moment of hope for Macbeth or not? Does hope require faith? This is one of those points where it's easy to get bogged down in definitions, so be clear and concise.
- Identify key points in the play that relate to despair and hope. Can either theme be followed throughout the plot? Are there specific events that epitomize either quality? Are these events limited to the characters, or do they extend to humanity, etc. as well? Macbeth is often seen as a critique of Man's fallibility, not just Macbeth's.
- Are any of these key points, or character's comments, directly related to hope or despair? For example, Lady Macbeth's "was the hope drunk, in which you dressed yourself?
So to summarize, you should define hope and despair, and set out the path by which this essay will investigate those themes - "Macbeth is a conflict between hope and despair; the hope of one man, and the despair of Man itself. Far from being faith in goodness, hope is herein characterized as ambition, lust and power. Hope has no redeeming values in Macbeth, but instead leads to ruin."
Once this has been established, begin providing narratives by which these themes can be investigated. Look at overall plot lines, such as Lady Macbeth's initial hope for power, and her eventual despair at her own inability to manage the guilt of her crimes, leading to her death. Look at Banquo's hopes compared to Macbeth's, look at MacDuff's despair when Malcolm tells him of the death of his children. Attempt to evaluate these storylines according to general messages; hope is eternal, hope is corruptible, despair leads to hope, and so forth.
Finally, bolster your points by looking at what the play itself says about these subjects; be careful not to spend too much time laying out your own ideas without letting the play do the work for you. Consider what Macbeth says about his faith in the witches, and his faith in himself. Look at Lady Macbeth's criticisms of Macbeth and the extremes to which she says she will go to attain her desires (dashing children's brains out and so forth).
I wanted to give you a good quote to work with in your essay. You'll have to figure out how to integrate this quote on despair on your own, but including a textual reference is essential in any great essay.
I have liv'd long enough: my way of life
Is fall'n into the sear, the yellow leaf;
And that which should accompany old age,
As honour, love, obedience, troops of friends,
I must not look to have; but, in their stead,
Curses, not loud but deep, mouth-honour, breath,
Which the poor heart would fain deny, and dare not. (act V, scene III)
"What would be the main points for writing an essay with the theme of hope and despair in relation to the play Macbeth?"
A very apposite question insofar as these pivotal themes always mingle through this play. Hope is truly present in this book but wears the garment of ambition. And this is where the sticking-point actually lies. Furthermore I think that despair is utterly embodied by the autexousious figure of Lady Macbeth. I've written an article on Macbeth : http://psittacismes.wordpress.com/2014/08/27/macbeth-a-hero-torn-between-reason-and-desire.