There is a thunderstorm. A weaponless man called Siegmund is fleeing and comes across a house: he is wounded and exhausted and cannot go on, so he decides to rest here. (It is possible that Siegmund does not know his own name yet). Sieglinde, who lives in the house, finds him and gives him water. She informs him that the the house and she herself belong to Hunding and that the guest should wait for the master of the house. Siegmund says that bad luck haunts him and that he must leave lest he should bring bad luck to the house but Sieglinde bids him stay: he cannot bring bad luck where bad luck already lives. Siegmund names himself "Woeful" and waits for Hunding.
Hunding arrives and greets Siegmund in a formal manner and then wants to hear his story. Siegmund tells his father was "Wolf" (he wore a wolfskin), and he had a twin sister. "Wolf" was very warlike and had many enemies. As Siegmund one day returned home, his mother had been killed and the home burned. His sister and father were nowhere to be found. He only found an empty wolfskin in the forest. Later he saw a damsel in distress: she was being forced into a marriage he did not want. Siegmund rushed into her defence and killed some of her enemies - only to learn they were actually her brothers and kinsmen. Siegmund fought, but was wounded and eventually lost his sword. The girl was killed and Siegmund had to flee.
Now Hunding declares that he was summoned to avenge on a murderer who had killed some people nearby and Siegmund turns out to be that murderer. Hunding says that his house will protect "Woeful" for today but that he must prepare to fight Hunding to the death tomorrow. Then he retreats to his bed - and Sieglinde mixes him a drugged drink, which will make him sleep heavily so she can meet Siegmund in private.
Siegmund is left alone. He remembers his father (whom he now calls "Volsa") promised him a sword when he most badly would need one - where is that sword now he asks. Sieglinde enters. She tells him she was forced into marrying Hunding against her will. Their wedding party had an uninvited guest: a fearsome stranger whose large hat was pulled down to cover one eye. Everybody except Sieglinde were afraid of him. The stranger had a sword and he thrust the sword in the tree trunk that is in the middle of Hunding's house and said that the blade would belong to anyone who pulled it out of the tree. Many have tried but none of them succeeded. (The appearance of the Valhalla leitmotif here makes it clear that the stranger was Wotan - just as he was "Volsa"). Sieglinde believes Siegmund is this person: the hero who would free her from her miserable life as Hunding's property.
They both reveal their true feelings to each other. Sieglinde reveals to Siegmund that she is his lost twin sister as well, and calls him his true name, Siegmund. Siegmund draws the enchanted sword from the tree and names it Nothung ("Needy"). They embrace each other passionately and the curtain falls.
Next:Die Walküre, Act II