Well, This is set after Star Trek (2009) but before Star Trek into Darkness.
Captain James T. Kirk was on the bridge of the USS Enterprise, sitting is the captain's chair and eating an apple. The Enterprise had launched from Star Fleet HQ on her new mission about two hours ago, and they were currently going toward the outer reaches of explored space.
"Captain, it appears that something has just appeared in the med bay." Sulu said.
"What do you mean something? What is it?" Captain Kirk demanded.
"It appears to be a blue police box."
Captain Kirk stood up and left the room at a run, heading for the med bay.
"Doctor where are we going?" Rose asked.
"Earth. 52nd century. I want to show you Star Fleet. They explore space and work peacefully with most alien species that they encounter. Although, they don't really encounter even close to all the different species there are."
The Tardis stopped moving and the Doctor offered Rose his arm. He opened the door and was greeted by the sight of phasers pointed at him.
"Come out of the box slowly." Captain Kirk said.
The Doctor stepped out of the Tardis and Rose followed, pulling the door shut behind her. The Doctor slipped his sonic screwdriver into his hand and locked the door, before tucking his screwdriver into jacket pocket.
Rose chuckled. "I thought you said they worked peacefully with alien species. Pointing weapons at us doesn't seem peaceful."
"Please explain who you are and how you came to be on our ship." Spock said, coming up behind Kirk.
"I'm the Doctor and this is Rose Tyler."
"Doctor Who?" Uhura asked.
"Just the Doctor."
"Okay Doctor, what are you doing on this ship?" Kirk demanded.
"We were traveling to Star Fleet Headquarters in my ship. It appears we missed our destination. You said we were on a ship?"
"Yes, this is the USS Enterprise, my ship."
"Why don't we sit down somewhere and I'll try to explain." The Doctor said.
The Doctor and Rose followed Kirk, Spock and Uhura to one of the empty rooms in the med bay. Kirk and Spock sat down in chairs, while the Doctor and Rose sat together on the bed with their hands intertwined and Uhura stood behind Kirk's chair.
"So who are you all?" Rose asked.
"I'm Captain James T. Kirk. This is Mister Spock and that's Uhura. Now, where are you from and how did you get here?"
"I'm from Earth." Rose said.
"I'm a nine hundred year old Time Lord from the planet Gallifrey. I am the last Time Lord, and my planet was destroyed in the Last Great Time War."
As the Doctor said this Spock smiled sadly. Rose noticed, and made a mental note to ask him about it later.
The Doctor continued speaking. "We arrived in my Tardis."
"What's a Tardis?" Kirk asked, frustrated that he had been talking to this Doctor for fifteen minutes and still knew almost nothing about him.
"Why don't you step inside and I'll show you."
The Doctor and Rose stood up and walked over to the Tardis. The Doctor placed a key in the lock and pushed open the door to allow Rose to go inside. He followed, beckoning for Kirk and his crew to do the same. Kirk decided to follow and gestured for Spock and Uhura to come with him.
"Doctor, it's a little box. How are we all supposed to fit?" Uhura asked.
Rose's voice echoed out from somewhere inside. "Trust me, we'll fit easily."
Kirk pushed open the doors and entered, followed closely by Spock and Uhura.
"It's -" Kirk began, only to be interrupted by Spock.
"It is smaller on the outside."
"Well that's new. Anyway, want to go on a trip." The Doctor said.
"Yes Doctor that would be pleasant." Spock said, curious to learn more about the strange blue box and its owner.
The Doctor flipped a few levers and turned a knob or two, while Rose held down a button. Suddenly a whooshing noise was heard throughout the control room and they were moving.
"Hang on; we're going to London, Earth, 2012 for the Olympics!" The Doctor shouted as the Tardis shook. Finally the Tardis stopped moving and the Doctor walked to the doors.
"The 2012 Olympics are taking place in London. The first event is in four hours and we have tickets. Well, we can get tickets." The Doctor said. Then he pushed open the doors.
And so the plot thickens.
I think everyone will meet in about four chapters. And then, well, you'll see.
Quick, grab the flying review over your head. Put it in the little white box at the bottom of the screen so it doesn't fly away again.