Dear English learners,

When responding to positive questions, students aren't usually confused (although some may confuse which verb to use):

A: Are you going to work tomorrow?
B: Yes, I am.
     or
    No, I am not. 

A: Do you have an umbrella?
    Yes, I do.
    or
    No, I do not.

A: Have you heard the news?
B: Yes, I have.
     or 
    No, I haven't. 

In positive questions, if you agree with the question you say 'yes', and if you disagree, you say 'no'. 

However, when responding to negative questions there can be more confusion:

A: Aren't you going to work tomorrow?
B: No, I'm not.

or

A: You're not going to work tomorrow?
B: No, I'm not.

If you agree with a negative question, you have to answer no. Some of my students say this is not natural for them. (They want to answer yes). 

If you disagree with a negative question, you have to answer yes:

A: You aren't going to work tomorrow?
B: Yes, I am going to work. 

A: You don't have an umbrella?
B: Yes, I do.

Note that if you're disagreeing with the negative question, you might put more emphasis on the verb to stress it. 

If you're agreeing with the negative question, you can also omit the verb and people commonly do in spoken English:

A: You aren't tired?
B: No (I'm not). 

The rest of the sentence will be assumed. 

Feel free to write your own negative questions and answers in the comments.