How do you put a conversation between 2 people in quotations?

Question

I'm not really sure as to how to do this. The conversation is "“’I’m George Milton. This here’s Lennie Small.’ ‘Glad ta meet ya,’ Carlson said again. ‘He ain’t very small.’ He chuckled softly at his joke.”

From Of Mice and Men

Is that done right? After the "Lennie Small" the speaker changes, so do I indent? Thanks.

Additional Details

I'm quoting their conversation. Like quoting the whole thing for use in an essay.

Answer 1

Best Answer - Chosen by Voters

It should look like this:

“I’m George Milton. This here’s Lennie Small."

"Glad ta meet ya," Carlson said again. "He ain’t very small." He chuckled softly at his joke.

Each speaker gets a new paragraph.