I will give you an example to write a CV.
This means that I will use the example to write a CV. Like "I will give you a pen to write a CV." It's awkward. It leaves the listener wondering what exactly you're going to give them.
I will give you an example how to write a CV.
This is missing a connector. What is the relationship between the example and how to write a CV?
I will give you an example about how to write a CV.
It's hard to make any sense of this. An "example" must be an instance of the thing it is an example of. So if this is in fact an example about how to write a CV, what would it be? A CV is not about how to write a CV. But nothing other than a CV is an example of a CV. So what could this be describing?
I could see one way this could be used.
Jack: I'm writing a book about how to write a CV. Do you have any examples of such books?
Jill: I will give you an example about how to write a CV.
It's awkward, but not incorrect (assuming the thing you're talking about is in fact about how to write a CV).
I will give you an example about writing a CV.
Same problem as above. What would be an example about writing a CV? A CV is not about writing a CV. And only a CV is an example of a CV.