When She Was Bad: Buffy comes back to Sunnydale after spending summer in LA with a bad attitude problem. Willow makes her attraction for Xander very clear to the viewers, although not particularly clear to Xander. When a bunch of (yes) particularly imbecilic looking vampires acquire the Master's bones, Buffy has to stop them resurrecting him, and work out her attitude problem at the same time. She accomplishes these two feats in one fell swoop, by hammering the Master's bones to dust.
No Assembly Required: A boy whose brother died while playing American football a few years back is discovered to be creating a Frankenstein-like body in the basement of his house. He chooses Buffy's high school foe, Cordelia, to supply the head. It becomes rapidly clear that his brother isn't as dead as everyone thought, and he has a Frankenstein-like body as well. He wants a female companion, which is what is being built for him. However, when Buffy intervenes, the brother returns to being as dead as everyone thought.
School Hard: It's parents' evening at Sunnydale High, and Principal Snyder is willing to tell Buffy's mum Joyce all sorts of lies about Buffy being a difficult child. However, a selection of vampires (who don't look quite as imbecilic as usual, due to them being led by Spike, a very cool vampire indeed) invade the parents' evening, and after Buffy fights them off, Joyce doesn't care in the slightest what Snyder tells her.
Inca Mummy Girl: An exchange student from Peru comes to stay at Buffy's house, but of course she isn't quite what she seems. This becomes rapidly obvious when she agrees to go out with Xander (an unusual event, in that no one except Willow seems willing to do this) and then shows that she is in fact a 500 year old Inca mummy, uh, girl. But Buffy kills her and it's okay.
Reptile Boy: Buffy and Cordelia become party mates for one evening to go to a fraternity party, Buffy going expressly against Giles' orders. At the frat party, the host drugs both Buffy and Cordelia and carts them off to the basement, where they are offered up as sacrifices to a very large reptile, which Buffy kills.
Halloween: A new fancy dress shop opens in Sunnydale, just in time for Halloween. Naturally, the owner of this shop has more on his mind than innocent trick-or-treating, and whoever wears these costumes turns into whatever they are wearing. Buffy becomes a 17th century noblewoman, Xander a soldier, and Willow a ghost wearing a tart's outfit (for some reason). The owner of the shop, whose name escapes me right now, although he does turn up in two episodes' time so perhaps I'll have remembered by then, is an old acquaintance of Giles', and it seems that Giles hasn't always been so squeaky clean as he likes us to think. However, he reverses the problems caused by his old friend and Buffy returns to her normal self, just before her 17th century noblewoman persona would have succumbed to a very vicious attack by Spike. And gosh, wasn't that a long episode synopsis?
Lie to Me: Buffy's old boyfriend from LA arrives to begin school at Sunnydale, provoking jealousy from Xander who, it should perhaps have been stated way back in The Witch, fancies Buffy. Obviously, this former boyfriend isn't a nice individual, as becomes clear when we discover that he has a deep longing to become a vampire. He traps Buffy in a basement and goes and gets Spike, as a reward for which he will be made a vampire. Fortunately, Buffy escapes, managing to lock Spike, his insane girlfriend Drusilla, a lot of other vampires and the boyfriend in the basement. The boyfriend does not survive.
The Dark Age: Giles' old friend pops up again and does something which I can't quite remember which makes a demon which Giles long ago helped create start to inhabit the body of Giles' girlfriend, Miss Calendar. After this experience, Miss Calender is substantially less eager to be Giles' girlfriend.
What's My Line, Part 1 (Part 1 of 2): Spike gets very annoyed at having to wait so long to cure Drusilla of her madness, and blames it all on Buffy. He arranges for some very tough assassins to kill her. But they don't. Buffy kills the first one by slicing his head off with an ice skate (ouch) and stops just short of killing the second when it is revealed that the second isn't an assassin at all, more someone called Kendra the Vampire Slayer. Kendra has also trapped Angel in a room filling with sunlight, and we are all terribly concerned about his welfare.
What's My Line, Part 2 (Part 2 of 2): Buffy and Kendra (who is in existence because of Buffy's death in Prophecy Girl) make a very good team as they go to fight Spike, who has, out of the kindness of his heart, released Angel and taken him to his secret headquarters. There, he allows Drusilla to torture Angel with holy water while they wait for the night, at which point they can complete the ritual which will stop Drusilla being insane by killing Angel. Fortunately (for Angel, less so for Spike) Buffy and Kendra turn up at the crucial moment and stop the ritual occurring. It seems that Spike and Drusilla are killed by a collapsing building, so the "Scooby gang", as they refer to themselves, go home very happy. Kendra goes away, back to wherever she came from.
Ted: Joyce gets a new boyfriend called Ted, who everybody except for Buffy likes. This dislike escalates until Buffy kills Ted. Fortunately, though, Ted wasn't a human at all but a robot. (But of course, Buffy didn't know that when she killed him! So is she guilty of murder or not?)
Bad Eggs: A school teacher decides to set his class a parenting project where they have to look after eggs very carefully for a week. As can only be expected, the eggs are not of the usual variety, more of a sort which hatch with evil little bugs inside them, which then take control of the person supposed to look after them. Buffy escapes this fate, and by killing the mother creature, cures everyone else as well.
Surprise (Part 1 of 2): Spike and Drusilla, not actually killed by the collapsing building after all, are engaged in an evil plot to reanimate the Judge, a demon who cannot be killed, whose sole intent is to destroy every good person in the world. On finding out about this plan, Buffy and Angel try to prevent it, but are too late. They make love and unfortunately this seems to have a distinctly bad effect on Angel, though we won't find out exactly what until next episode.
Innocence (Part 2 of 2): The gypsy curse on Angel is lifted, taking his soul away, as a result of one moment of pure happiness. When it becomes painfully clear to Buffy that Angel is now once again Angelus, the evil vampire of days gone by, she realises that she must kill him. Meanwhile, Xander concocts a plan to defeat the Judge - blowing him into his component atoms with a grenade launcher. Willow discovers his and Cordelia's secret relationship and is very upset.
Phases: The gang find out that Willow's boyfriend Oz is a werewolf and the school womaniser Larry is gay. That synopsis was very short to make up for the very long ones I've been doing.
Bewitched, Bothered and Bewildered: Cordelia breaks up with Xander on Valentine's Day, leading Xander to try to get Amy (from Season 1's 'The Witch') to cast a love spell on Cordelia for him. Unfortunately, it backfires and every woman in Sunnydale, except Cordelia, fall madly in love with him.
Passion: Miss Calendar attempts to find a way to restore Angelus' soul, and manages to come up with a method. Unfortunately, before she can tell anyone, Angelus finds her and murders her. Buffy determines that she must kill him. The disk on which Miss Calendar stored her plan to restore Angelus' soul falls out of sight, but almost certainly not forever.
Killed By Death: Buffy, sick with a raging fever, is admitted to Sunnydale hospital, where she is able to see a demon normally invisible to grown-ups, because she has the fever. This demon, der Kindestod (quite why it's given a German name is not explained), feeds off sick children. But Buffy kills it, so it's okay.
I Only Have Eyes For You: A poltergeist haunts the school, forcing Buffy and the others to exorcise it. Meanwhile, Angelus and Spike are increasingly at odds with one another.
Go Fish: The Sunnydale High swimming team are inexplicably turning into fish monsters and killing people. Xander thus joins the swimming team in an attempt to find out what's going on, and nearly turns into a fish monster himself. But he manages to not turn into a fish monster, so it's okay.
Becoming, Part 1 (Part 1 of 2): Angelus and Drusilla steal an entombed ancient demon which will apparently create hell on earth once activated. Angelus tries to activate it but fails, but does manage to lure Buffy away from the library for long enough for Drusilla to kidnap Giles and kill Kendra, who popped up at the start of the episode.
Becoming, Part 2 (Part 2 of 2): Angelus spends some time torturing Giles for no particular reason. Spike works to help Buffy stop Angelus, but leaves town instead. Willow works on a ritual to restore Angelus to his former status as nice vampire, and succeeds. But Buffy kills him anyway, and then runs away to LA.