いいえ indicates that the speaker does not confirm the other person's assumption. Therefore, when asked a negative question and the answer is different from the questioner's assumption(i.e., you wish to negate the questioner's assumption expressed in the negative form), use いいえ and make an affirmative statement. Note that the reply would begin with "Yes" in English in situations like these.
A: マナさんは いませんか。
Isn't Mana there?
B: いいえ、マナさんは います。
Yes, he is.[That Mana is not here is wrong].
A: 冬休みは みじかく ないですか。
Isn't winter vacation short?
B: いいえ、冬休みは みじかいです。
Yes, it's short.
A: あさっては 休みでは ありませんか。
Isn't the day after tomorrow a holiday?
B: いいえ、あさっては 休みです。
Yes, it's a holiday.