The story starts with the Doctor and Jamie looking for the TARDIS, which has been stolen. If Admiral Ackbar had been there, he'd have told them it was a trap. Scientists Maxible and Waterfield were doing time travel experiments, and the Daleks showed up, took over, and took Waterfield's daughter Victoria hostage. So the Doctor and Jamie end up back in 1866 at Maxible's house, and there are the Daleks.
The Daleks keep getting beaten by humans, so they want to find out what that "human factor" is, distill it, inject it into themselves, and become invincible. This is logical in Dalek brains, I guess? The idea is that Jamie has to rescue Victoria and the Doctor will record his emotions as he goes along his quest. Again...we're stretching here, but this is still a fantastic story.
The Doctor puts the "human factor" emotions into three experimental Daleks, gives them names, and teaches them that they're his friends. Then they all head to Skaro, with the Daleks thinking that this is brilliant and definitely not going to backfire at all.
It goes as expected when you put human emotions in a Dalek...they question orders and all hell breaks loose. The Doctor fools more Daleks into accepting good human emotions, and then they all start fighting each other and attacking the Emperor Dalek, which looks pretty crazy.
Skaro is visited again and again in Doctor Who, and it always looks different...Anyway, the Doctor thinks this is the final end of the Daleks, but we know they keep popping up in the future. Victoria's father dies, so she joins them in the TARDIS at the end.
This is a terrific story. If it weren't almost completely missing, I think it would be a classic.
Companions: Jamie, Victoria
Episode: #36, "The Evil of the Daleks," seven parts
Adversary: the Daleks
Classic Lines: a Dalek, ordering Victoria not to feed the birds at the window: "You will not feed the flying pests outside."
Tuck This Away to Impress Your Friends: The Daleks won't be seen again for another four years. They next face the 3rd Doctor in "Day of the Daleks."
Next Up: "Tomb of the Cybermen"