The others find them unwittingly playing exhibits in a wax museum of sorts in a castle on the planet:
Obviously, a pre-cursor of both Q and Ngillum, the guy who owns this castle is obsessed with the Earth of 900 years earlier, because he's 900 light years away. He plays the pianoforte and studies the classics. He wants to know about the Enterprise's battles and conquests. He operates the castle as a little oasis in an otherwise hostile environment.
Kirk challenges the guy to a duel to buy time while Spock figures out the source of Trelane's power. Kirk shoots his mirror, which is one of the sources of his power, but Trelane still has his mojo, so he puts Kirk on trial.
Kirk convinces Trelane it would be more fun to have another duel. Trelane wears his sword and his Marshall Ney boots and chases Kirk around the forest. Finally, Trelane's parents come and recall him, allowing Kirk and the others to escape.
