Knowing when to use 不 and when to use 没有 can sometimes be difficult, but with that being said, there are some relatively easy ways to figure out which you should use.

First, in Chinese you often confirm an answer by repeating the verb and negate by repeating the verb with either 不 or 没有. Knowing when to use which one is often based on the question you were asked.

Examples:
Using 不:
Question: 你晚上会不会去打球？or 你晚上会去打球吗？(Are you going to play ball tonight?)

Answer: 去 (Yes) 不去 (No)

Question: 你下个星期四想不想一起去吃晚饭？or 你下个星期四想一起去吃晚饭吗？ (Do you want to go to dinner together next Thursday?)

Answer: 想(Yes) 不想 (No)

Using 没有:
Question: 你有没有空？ or 你有空吗? (Do you have time)

Answer: 有空 (Yes) 没有/没有空 (No)

Question: 你有没有我的手机？or 你有我的手机吗？ (Do you have my cellphone?)

Answer: 有 (Yes) 没有 (No)

Question: 你上个周末你跟他们去了吗？(Did you go with them last weekend?)

Answer: 没去 (No)

*****As these examples show 不 is often used to negate answers about actions in the present and future, while 没有 or 没 is used to negate questions about action in the past tense and possession.