A quick unintentional stop in the Mandragora Helix inadvertently leads to some Mandragora Helix energy getting aboard the TARDIS, which then takes the TARDIS to 15th-century Italy. ("Strange," the Doctor remarks. "Forced landing. ... I didn't touch a thing.") The Helix energy gets out, which leads to some rather nifty special effects as the energy (which appears to be a red light superimposed on the screen) moves things around and causes explosions and death (the sizzling of the water being a particular favorite of mine). They did a really good job of making it seem like the light is actually interacting with things on the location.
The time period was well chosen by the Helix, it seems; writer Louis Marks (in his final script for the series) is making the point that this time is, as the Doctor says in part two, "the period between the dark ages of superstition and the dawn of a new reason," and thus the perfect time for the Helix to invade, as it uses the vestiges of one of the ancient religions (the cult of Demnos -- not a real cult or pagan figure, in case you were wondering), on the verge of being wiped out, as the way to cement its power on Earth.
Most of the first episode involves exploring 15th-century Italy, making our way to the seat of power in this area. Count Federico seems to be the de facto ruler of San Martino (not a real dukedom), with little interest in the new science that the actual Duke, Giuliano, is engrossed in, but little regard for superstitions -- if he can't use it toward his own end, Federico doesn't care. That includes the Doctor, who's trying to warn them about the Helix ("A ball of heavenly fire has come down to Earth. It could consume everything in its path. It could destroy the world"). Federico decides he's of no use and sends him to be executed...
Well, of course he manages to escape, where he not only rescues Sarah from the clutches of the Cult of Demnos but also meets up with Giuliano. While rescuing Sarah though, he watches as the Helix energy descends upon the Cult -- it seems that the Helix has been communing with Hieronymous, Federico's court seer and the leader of the Cult, and the Doctor provided the Helix with the opportunity to reach Earth. We also see more evidence of the effect Helix energy has on people -- turning their skin into a bright blue substance, rather like a form of copper oxidation. But that's about it for this episode, and the cliffhanger is rather lackluster, as it simply involves Sarah being recaptured by the Brotherhood of Demnos; that said, the high priest's final line of the episode -- "Demnos will not be cheated of his pleasure, little one" -- is suitably menacing in its calmness.