How do I address exam questions? For example 'How does Shakespeare present madness in King Lear?'

Answering this question is a matter of technique as much as it is about knowledge of the play. Madness is a capacious term in King Lear, therefore, in order to produce a focused and well argued essay (as required in the exam) I would recommend concentrating on specific examples, and statements which link together to form an overall argument. This narrows the scope of the essay and ensures the question at hand is throughly addressed.
For example, we can produce several statements which can be evidenced with quotations from the play and secondary material as required in the assessment criteria for the exam. These could be, but are not restricted to: 'Shakespeare suggests that Lear's abdication of his kingdom is a kind of madness.''Lear's madness demonstrates Shakespeare's concern for a strong monarch''In Lear's madness he is blessed with insight - he sees the injustice of the world''His madness reveals the the world is unreasonable - it is a true madness to see order in the world.''Shakespeare suggests that there is reason in madness, and madness in reason'
This template is the technique that I would recommend. Once this preparation format is adopted, the matter of learning content clarifies itself. The potentially intimidating prospect of producing an exam essay on the spot is overcome as the examples are prepared and well stored in the candidates mind.