“Round trip, please.”
Round trip means travel to a destination and back; one way means travel in one direction only. Since round can also describe a circular shape, Tina thinks the train will go around in a circle. Frank's Do you understand? checks that the explanation has reached her.
“at six in the morning”
This means "at 6 a.m." At six alone could mean morning or evening, so in the morning makes it clear. They are taking a day trip to Kyoto, so they catch a morning train.
“Fine. A circle. Now follow me.”
Here Fine. means "okay, have it your way," and follow me means come with me. Even after Frank explains a round trip, Tina insists it is a circle. The punchline is that Frank gives in, says "A circle," and heads for the platform.