Usage of 没有

Usage One:
没有 basically means 'not have'. Here 有 functions as a verb which means 'to have'; and 没 functions as an adverb to negate the verb.
For example,
A-- Do you have a pen?
       你有笔吗？
B-- I don't have a pen.
      我没有笔。

Click the following video to hear the sound:

Sometime, we shorten 没有 as 没. So the dialogue above can also be:
A-- Do you have a pen?
你有笔吗？
B-- I don't have a pen.
我没笔。
Click the following video to hear the sound:

Usage Two:
没有 functions as auxiliary to negate the verb in past tense and perfect tense. It can also be shortened as 没。
For example,
I didn't eat breakfast this morning.
今天早上我没有吃早饭。
or
今天早上我没吃早饭。

I haven't gone to China.
我没有去过中国。
or
我没去过中国。
Click the following video to hear the sound.

The phrase 没有关系 is highly frequently used in our daily life. It means 'it's okay/ it's alright '
For example,
(Person A stepped on person B's foot by accident.)
A--  Sorry.
对不起。
B-- That's alright.
没有关系
or
没关系。

Another example,
Student--  Sorry, I didn't do homework.
对不起，我没有做家庭作业。
or
对不起，我没做家庭作业。
Teacher -- It's okay.
没有关系。
or 
没关系。
Click the following video to hear the sound: