Before TPM the common assumption in both the fandom and in the few EU sources that touched on the subject (though the PT era itself was off-limits by decree of Lucas for a long time) was something like this:
The Clone Wars were a series of conflicts that occurred about 35 years before ANH.The Clones were the bad guys and also mentally unstable because of being grown too fast. One of the villains creating the Clones was a warlord named Atha Prime (who did eventually sorta make into Legends as a genetic terrorist).
Other bad guys of the period included a bunch of Dark Jedi from Bpfassh.The Clone Wars left the Republic on the verge of collapse, which Palpatine exploited to become President and then Emperor; this process took several years.\Obi-Wan was trained by Yoda; one day he met Anakin and took it upon himself to train him. But before Anakin's training was completed, they had a falling out which led to them fighting and Anakin falling into a molten pit.
Luke and Leia's mother might have been a Fallanassi Adept who abandoned her people's pacifism to fight with the Jedi for the Republic, during the course of which, she met, fell in love with, and married Anakin. She died of unknown causes when Leia was young, but still old enough to have some memory of her.The Jedi allowed families and had no fixed facilities, but instead flew around in mobile academies like the Chu'unthor.
Palpatine, through means unknown, betrayed and wiped out the Jedi as part of his ascension to Emperor.The Empire was established at some point AFTER the Ghorman Massacre, by which point the three founders of the Rebel Alliance were already plotting the rebellion.
"Obi-Wan made one last try to save Anakin from the dark side, but Anakin drew his Jedi weapon-the lightsaber, with its blade of pure energy. Obi-Wan reluctantly raised his own lightsaber in defense, and the two battled near a pit of molten lava. During the fight, Skywalker fell into the molten pit. But Anakin Skywalker did not die. He emerged from the pit a scorched shell of a man, full of hatred. In that dark moment, Anakin was transformed."
Obi-Wan: "When I first encountered your father, he was already a great pilot. But what amazed me was how strongly the Force was with him. I took it upon myself to train Anakin in the ways of the Jedi. My mistake was thinking I could be as good a teacher as Yoda. I was not. Such was my foolish pride. The Emperor sensed Anakin's power, and he lured him to the dark side. My pride had terrible consequences for the galaxy."
Luke: "There is still good in him."
Obi-Wan: "I also thought he could be turned back to the good side. It couldn't be done. He is more machine, now, than man -- twisted, and evil."
Luke: "I can't kill my own father."
Obi-Wan: "You should not think of that machine as your father. When I saw what had become of him, I tried to dissuade him, to draw him back from the dark side. We fought. Your father fell into a molten pit. When your father clawed his way out of that fiery pool, the change had been burned into him forever -- he was Darth Vader, without a trace of Anakin Skywalker. Irredeemably dark. Scarred. Kept alive only by machinery and his own black will. [...] When your father left, he didn't know your mother was pregnant. Your mother and I knew he would find out eventually, but we wanted to keep you both as safe as possible for as long as possible. So I took you to live with my brother Owen on Tatooine...and your mother took Leia to live as the daughter of Senator Organa, on Alderaan."
- Return of the Jedi novelization.
In an interview in Starlog in 1980, Mark Hamill recounts a background story which he had been told: "I remember very early on asking who my parents were and being told that my father and Obi Wan met Vader on the edge of a volcano and they had a duel. My father and Darth Vader fell into the crater and my father was instantly killed. Vader crawled out horribly scarred, and at that point the Emperor landed and Obi Wan ran into the forest, never to be seen again."