Ian: Where did you get hold of this [brooch]?It's time for another historical episode, as the TARDIS materialises inside an Aztec tomb. The Aztec era happens to be one of Barbara's specialties, and she loves the tomb's shiny trinkets so much that she immediately puts one on. Upon emerging from the tomb wearing the snake bracelet, Barbara is hailed as the reincarnation of the Goddess Yetaxa. Oh, and the door to the tomb shuts itself behind them.Despite the Doctor's very stern warnings, Barbara seizes the opportunity to influence history. Her intentions are good (she decrees an end to the practice of Human Sacrifice), but she instantly makes one of the high priests suspicious of her alleged divinity and pitches the other one headlong into a crisis of faith. Barbara finds that even a goddess can't effect social change by fiat.Meanwhile, the Doctor is told to rest in the serene gardens together with the rest of the old folks. He befriends Cameca, an very sweet Aztec woman, who turns out to know the son of the tomb's architect. Seeing a way out, the Doctor spends more and more time with her... and accidentally gets engaged when he makes a cup of hot cocoa.Ian, off on his own, actually meets the son of the tomb's architect, who immediately takes exception to him — having been the champion of the Gods until Ian arrived. Ian is forced to fight him in judicial combat, and the Doctor, hoping to get his hands on the tomb's blueprints, unwittingly helps the guy (not knowing that Ian will be his opponent). Luckily, Ian turns out to be pretty damn Bad Ass and can easily hold his own in combat.In the middle of all that, Susan is sent off to a seminary for proper education, and gets into an Arranged Marriage as part of a plot by Tlotoxl to trap and discredit Barbara.In the end, the Doctor bids Cameca farewell, lashes up a pulley wheel to open the massive tomb door and let them back in to escape in the TARDIS. Barbara didn't convince anyone to stop human sacrifices, but her priest friend at least managed to separate himself from Aztec society and became a hermit instead.
The Doctor: My fiancée.
Ian: I see ... your what?
The Doctor: Yes, I made some cocoa and got engaged.