The Doctor, Amy and Rory arrive on a pirate ship, apparently because of a distress signal they received. The distress signal will be relevant later, but given how often stupid shit like that happens in this show for no reason there's no way to guess that.
But it turns out there's a siren (which they sometimes call a mermaid even though she clearly isn't) taking people from the ship. Anyone who gets even tho slightest injury gets vanished. This is demonstrated as Rory and a random crew-member get cut when Amy sword-fights with a pirate. Apparently sword-fighting is easy, anyone can do it. Even though this is a ship full of pirates who have presumably been using swords for a while now, Amy manages to fend them off quite easily.
So then the siren comes to take Rory and the crewman. They manage to hold Rory back and keep him from being taken, but apparently no one thinks it's worth bothering trying to save the crewman, so he just wanders off and gets taken.
They run around for a while trying to find a safe place to hide from the siren, eventually figuring out that it can teleport out of any reflective surface at any time, but mysteriously doesn't. No one seems to notice that it's being extremely selective about what it teleports out of and it's never brought up, so presumably it's just a giant gaping plot hole.
In trying to find a safe place to hide they end up discovering that the captain's son has stowed away on board. And has managed to survive, even though the crew had been rationing the drinking water. How the boy got the key to the normally locked room they found him in and how the missing key to the powder store or the fact that the door wasn't locked had gone unnoticed is never mentioned.
The Doctor and the captain then go to get the TARDIS (which was the first place I thought of when they were looking for somewhere to hide, but I guess there's no way the captain's son could have been hiding there so they had to go somewhere else first), but find that it's not working, and then it gets stolen by the siren. As it's being stolen, the Doctor and the captain have time to get out, which they do for some reason, leaving them trapped on the ship.
Then there's a storm and Rory gets knocked overboard, so the Doctor decides to set the siren on him to prevent him from drowning, because he now believes that the siren isn't killing people, just taking them somewhere, even though he has no apparent reason for believing that. On the same basis, he gets Amy and the captain to cut their fingers and does the same himself so the siren will take them.
Obviously the Doctor is right and they find themselves on an alien space-ship that is somehow in the same place as the ship, but in a different dimension or something. The crew are dead, killed by an Earth virus. Earth viruses have never been a problem for any other aliens, but for some reason these particular ones are susceptible to them.
They then discover that all the people the siren took are in stasis pods, because the siren is some sort of automatic medical system. But for some reason it never put the original crew into stasis, and it didn't put the Doctor, Amy or the captain into stasis. No explanation is offered for this inconsistency.
And the reason that everyone's still in stasis is that the siren doesn't know how to heal humans. But it won't let them take Rory out of stasis because he'll die if they do. Until they convince it that they'll sign a waiver accepting responsibility for him or something.
Somehow they're able to wake Rory up without him dying, but can't move him, so he teaches Amy how to perform CPR on him once they unplug him. Even though I'm pretty sure the Doctor would A) already know how to do CPR and B) have some pretty advanced medical equipment in the TARDIS.
Oh, and by the way, how exactly can Rory drown anyway? He's a robot. He's been a robot since the end of last season. The real Rory was erased from history. This one's a robot copy. He doesn't need to breathe. He's a robot.
Anyway, they save Rory, but then they can't return the pirates to Earth because the captain's son has typoid fever and will die if they take him out of stasis. Oh wait, no, actually he's fine as long as he stays on the spaceship. Even though that is not at all how it worked for Rory. And even though that makes no fucking sense. If the spaceship can make him healthy, why can't he just go back to Earth healthy? If it can't, how can he leave stasis?
Anyway, the pirates decide to stay there and become space pirates, I guess, and the Doctor, Amy and Rory leave on the TARDIS. And then right at the end of the episode they throw in the little reminders of the season-long plot arc, Amy and Rory talking about how they can't tell the Doctor about how they saw him die and the Doctor looking at the test results that show that Amy both is and is not pregnant.
And seriously, am I the only one who remembers that Rory is a robot? I can't be because they explicitly mentioned it last week. How did no one catch this?