I'm not sure what you're asking. But the two lines should read: Person 1: "I'd like a copy of today's paper, please." Person 2: "I'm afraid we've sold out." What part of these sentences are you having problems understanding?

I'd like a copy of today's paper, please. I'm afraid we've sold out. sell out = bán hết hàng paper = newspaper "a copy of [name of newspaper]" is the correct way to indicate one unit. Newspapers come in "copies". A copy of The Times. A copy of The Guardian. A copy of today's newspaper. This last one is a bit strange, as there are many kinds of newspapers.