Here's a good one from "Who Watches the Watchers" (season 3, episode 4):
Picard has to convince someone that he is not a god. He has to lead that person to a particular worldview.
"Look at me...feel the warmth of my hand, the rhythm of my pulse. I'm not a supreme being. I'm flesh and blood, like you."
"Not like me."
"Like you. Different in appearance, yes, but we are both living beings. We are born, we grow, we live, and we die. In all the ways that matter, we are alike."
- Picard and Nuria, just after Nuria is beamed aboard the Enterprise
"Nuria, your people live in huts. Was it always so?"
"No. We have found remnants of tools in caves. Our ancestors must have lived there."
"So why do you now live in huts?"
"Huts are better. Caves are dark and wet."
"So if huts are better, why did you once live in caves?"
"The most reasonable explanation would be that at one time we did not know how to make huts."
"Just as at one time, you did not know how to weave cloth, how to make a bow..."
"That would be reasonable."
"Someone invented a hut. Someone invented a bow, who taught others, who taught their children, who built a stronger hut, who built a better bow, who taught their children. Now, Nuria, suppose one of your cave-dwelling ancestors could see you as you are today. What would she think?"
"I don't know."
"Well, put yourself in her place. You see, she cannot kill a Hornbuck at a great distance. You can, you have a power she lacks."
"Only because I have a bow."
"She has never seen a bow. It doesn't yet exist in her world. To you, it's a simple tool. To her, it's magic."
"I suppose she might think so."
"And how would she react to you?"
"I think she would fear me."
"Just as you fear me."
"I do not fear you any longer."
"Good. That's good. You see, my people once lived in caves, too, and we learned to build huts...and, in time, to build ships like this one."
"Perhaps one day, my people will travel above the skies..."
"Of that, I have absolutely no doubt."
- Picard and Nuria, in the Enterprise observation lounge
Logic, emotion (strength, empathy, etc.), the socratic method, etc...