How exactly do exploits get found?

How exactly do exploits get found?

How do hackers find exploits? ( Detailed explanation please )

and, how do they use the exploits? ( Detailed Description please )

I am writing an article for a New Zealand Internet Safety website... and also a report for an ecrime department here.

I will not be using this information for illegal purposes, its strictly for educational purposes ONLY.

Thanks.

 

 

 

 

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