Before going to, quote, "Space: 1969", everybody goes on a picnic. It's discovered that the Doctor we're dealing with is 1103, or about two hundred years older than the Doctor we've been dealing with since Eccleston. The Doctor complains about the taste of wine because he's never had wine before in 1100 years. He calls Amy fat, in that charming way British people treat each other in the Moffatverse, and then Amy sees a skinny man on a butte. She forgets that he's there the second she looks away, so the Doctor says more needlessly cryptic stuff.
Question: Where is Doctor 1103's TARDIS?
A mystery person drives up in a van -- Canton Delaware III, as played by Mark Sheppard's father -- and the Doctor waves to him. Meanwhile, a mysterious astronaut comes out of the picnic lake, weirding River out. The Doctor approaches him/her/it and tells everybody to stay back: "Whatever happens now, you do not interfere. Clear?"
Up close, sad Doctor says, "Hello. It's okay, I know it's you." He or she or it raises the faceplate, and he nods. "Well then?" He bows his head, and the astronaut shoots the Doctor in the head, and then a couple more times. River and Rory hold Amy back, as per, and the Doctor starts regenerating. So far, this all seems to be according exactly to the Doctor's plan, but there's nobody onscreen who seems to take comfort in, or even understand, this obvious fact.
The Doctor and Amy lock eyes and he apologizes, but before he can complete his regeneration... The astronaut shoots him again. So now the Doctor is just dead. River pulls out her tricorder to confirm it, and then takes aim at the astronaut, who's heading back into the lake. "Of course not," she says to herself, and then goes back to crying Amy. All of this will make sense and/or matter later, but not next week.
Old stranger Canton takes off his hat and gives them a gascan, which River explains: "A Time Lord's body is a miracle. Even a dead one. There are whole empires out there who'd rip this world apart for just one cell. We can't leave him here. Or anywhere."
Amy yells at the dead Doctor about how he's a "stupid bloody idiot," and begs Rory to help her figure this out. River says they need to "do what the Doctor's friends always do: As [they're] told," and Rory notices a random boat on which they give him a Viking funeral while the music goes nuts. Eventually Rory stumbles back onshore and there are lots of sad looks at everybody from everybody.