Dialog:

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A:  What do you think about all the coverage of the Royal Baby? B:  It makes me sick!  I really don’t see what the big deal is.  A:  I think mostly women care about it from what I’ve seen.  Maybe they fantasize about marrying a prince or something.  They get all emotional about this kind of fairy tale life.  It also helps that Kate is pretty hot.  William, on the other hand, looks terrible, but at least he has a good sense of humour about it and said he was glad the baby takes after his mom in terms of how he looks.  B:  Well, I guess if it’s just girls who care about it then it’s not too bad.  I certainly wouldn’t want to be friends with any guy who genuinly gives a damn about this.

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Coverage:  In this sense, "coverage" is talking about "media coverage".  This means how much a story is on TV, in the news, written about online, in newspapers, and in magazines.  If a story is written about and talked about a lot, it has a lot of coverage.  If it wasn’t written about or talked about much, it didn’t get much coverage. 

It makes me sick:  This is a great phrase to use when someone or something really bothers you or annoys you.  If you hate something about someone or something, just say that "they" or "it" makes you "sick".

It makes me sick that professional athletes make so much money.
I don’t want to listen to that guy anymore.  He’s such a liar and a fool.  He makes me sick.
I can’t believe all the garbage that’s on TV.  It absolutely makes me sick.

Fairly tale life:  A "Fairy Tale" is a happy children’s story where everything is wonderful and has a happy ending.  It’s like a fake wonderful life. 
"Cinderella", "Snow White", and "Alice in Wonderland" are all examples of fairy tales. 
If someone wants a "fairy tale life" it means they want some kind of wonderful life that is impossible to achieve and totally unrealistic.  The Royal family’s life is almost like a fairy tale life, because they are the only people in the world that have such an easy life since they were born.

Good sense of humour about it:  If you have a "good sense of humour" it means you are funny and recognize good jokes.  You like to laugh. 
If you have a "good sense of humour about something" it means that you can laugh at some weakness about yourself.  It’s a very good character trait.

Takes after his mom:  If you "take after" someone, it means that you are similar to them in some way.  We often use this when talking about people’s children.  We say that someone "takes after his father" or "takes after her grandmother" in some aspect.
If you "take after" someone in terms of appearance, it just means that you look like them.

"He really takes after his grandfather.  They are both super lazy and love to drink beer".

Genuinly:  If you "genuinly" like something, it means that you are serious about it, and you are not faking it in any way at all.

I think don’t think he genuinly likes shopping, but he just pretends to so he can make his wife happy.

Gives a damn:  If you "give a damn" about something, it means that you care about it.  If you "don’t give a damn" about something, it means that you don’t care about it at all, and have absolutely no interest in it.

I really don’t give a damn about what other people think of my lifestyle choices.  I’m going to do whatever makes me happy.