Saying ‘Yes, I do. / No, I don’t’ in English is more polite than just saying ‘Yes. / No.’ That’s why short answers are very commonly used.
To form the short answer, you use the first word from the question. (This is either an auxiliary verb or a form of ‘be’.)
Use the long form (he does) in affirmative answers (yes).
Use the short form (he doesn’t) in negative answers (no).
Question Affirmative Negative
Do we know him? Yes, we do. No, we don’t.
Can she see me? Yes, she can. No, she can’t.
Have they read the book? Yes, they have. No, they haven’t.
Is he hungry? Yes, he is. No, he isn’t.
Will he work? Yes he will No he won't
Mind: If ‘you’ is the subject of the question, ‘you’ must be replaced by ‘I’ or ‘we’.
Question Affirmative Negative
Do you know him? Yes, I / we do. No, I / we don’t.
If the question starts with ‘are you’, ‘are’ must sometimes be replaced by ‘am’.
Question Affirmative Negative
Are you hungry? Yes, I am. No, I’m not.
But: → Yes, we are. No, we aren’t.