I get confused when someone asks me a negative question like ‘Don’t you want a drink?’ instead of ‘Do you want a drink?’ How can I know if I should say ‘Yes’ or ‘No?’
Reiji, Japan.

Good question Reiji. Over many years of teaching I have noticed that this is an area that causes difficulties for a lot of students. Only the other day, as a joke, I asked a class ‘Wouldn’t you like me to give you extra homework tonight?’ I was very surprised when the whole class answered in one voice ‘Yes!’
I knew that they did not want more homework so why did they give this answer? My students were confused because the question was not the usual one that they were used to i.e. ‘Would you like me to give you extra homework tonight?’ As a result of this confusion, they said ‘Yes’, when really they meant ‘No!’
Fortunately the way to avoid this confusion is very simple. In English Yes/No questions are usually positive as in the following typical conversation:

A. Do you know what the capital of Brazil is?
B. Yes, (I do). It is Brasilia. (Positive answer)
Versus
No, (I don’t). What is it? (Negative answer)

However, we can change any Yes/No question into a negative question if we want to emphasise the question or express surprise:

A. I’d love to go to Rio de Janeiro, the capital of Brazil.
B. That’s not right! Don’t you know what the capital of Brazil is?
A.   Yes, (I do). It ‘s Brasilia. That was a slip of the tongue! (Positive answer)

Versus
No, (I don’t). I thought it was Rio! (Negative answer)

The trick is to remember that although the question may be positive or negative, your answer does not change, the answer depends on you not the question. Thinking about the auxiliary that follows the word ‘Yes’ or ‘No’ helps too, please note that, as in both conversations above, the auxiliary must always be positive if your answer is ‘Yes’ and negative if your answer is ‘No.’
In other words ‘Yes’ always means yes and ‘No’ always means no!