Episode 1
Evangelion .. Episode synopses .. Episode 1 "Angel attack"
A teenage boy Shinji is called to meet his father for the first time since he was three years old. He arrives in Tokyo-3 to await the arrival of Misato, a woman from his father's work who is supposed to meet him, but a fight with a gigantic monster commences nearby just as she arrives, and they are both almost killed... they escape and make their way to NERV. Misato is... not quite what Shinji had expected.
Shinji finally arrives at his father's workplace, NERV, only to discover that he is expected to pilot a huge bio-mechanical robot called an "Evangelion" against the monster outside that almost killed him - an "Angel". He is reluctant to do so, until he sees the only other option for a pilot; a girl his age who is badly injured and obviously unable to battle. He finally accepts the mission, and gets into the EVA ready to fight...
Episode 2
Evangelion .. Episode synopses .. Episode 2 "Unfamiliar ceiling/The beast"
Following the battle, Shinji is taken in by Misato, and goes to live at her apartment (which is a little shocking; she has a pet penguin, and fifty gallons of beer in her fridge!). Seems strange that the battle never finished? No problem - there are flashbacks that show what happened... Shinji marched out in the Evangelion, with absolutely no idea of how to fight, and was soon at the mercy of the angel Sachiel.
The angel managed to hurt him pretty badly, but just when it seemed that Shinji was finished, the Eva went bezerk and promptly began to kick the angel into next week. Finally realising it was about to be defeated, the angel self-destructed in an effort to destroy Shinji and the Eva... but the robot emerged from the explosion, still intact (although then it's head falls off).