The majority of the back story for the Wizard of Oz is provided in Dorothy and the Wizard in Oz, following up on the brief bit of history we get in The Wonderful Wizard of Oz. He was born Oscar Zoroaster Phadrig Isaac Norman Henkle Emmanuel Ambrose Diggs, and used his first two initials because the rest of them spelled "pinhead."
He was born in Omaha, the son of a politician, and joined the circus at a young age. During his circus career, he worked as a ventriloquist, a stage magician, and a balloonist. When his balloon, on which was emblazoned the initials O.Z., landed in the Land of Oz, the people took him for a member of their royal family. He also claimed to be a wizard, and showed them some magic tricks. Soon, he had managed to make himself ruler of the country, although his actual power didn't extend much beyond the Emerald City that he had built, presumably on the ruins of King Pastoria's old castle.
After many years of hiding out in his palace, Dorothy and her friends discovered his secret, and he left the land in a balloon. He eventually returned to Omaha and again worked as a circus balloonist until getting caught in a California earthquake and falling into the subterranean Vegetable Kingdom. It just so happened that Dorothy had also ended up there, and she helped him reach Oz, where he remained and trained under Glinda to learn real magic.
This was actually a pretty solid history for the most part, although there are a few questions remaining. I've already looked at how sinister the Wizard's motives were and the origin of the Nine Tiny Piglets, but there are others. For instance, when did the Wizard arrive in Oz? He claims in Wizard to have grown from a young man to a very old man while there, but how many years was it? It would be interesting to know when he left the United States relative to the Civil War and to his native Nebraska becoming a state in 1867. The short story "Buffalo Dreams" has him leaving for Oz sometime in the 1890s, but I'd say that's not enough time.
We do know that he arrived in Oz at a time when two Good Witches and two Wicked Witches controlled most of the country. At one point, he was driven out of the West by the Winged Monkeys. Mombi was no longer in power, but still active, and Oscar had dealings with her. This situation is clearly different from what we see in Wicked, in which Elphaba and Nessarose don't obtain any kind of power until after the Wizard has set up his totalitarian government. It sort of looks like the upcoming Oz, the Great and Powerful will also take this route, but I obviously couldn't say for sure.
It's curious to note that, while the Wizard is a character with an established full name (unlike, say, the Shaggy Man), hardly anybody ever uses it. When he was ruling, he went by Oz, which makes sense given the case of mistaken identity. After his return, however, pretty much everyone just calls him "Wizard" as if that were his name.
Another interesting thing is that Oscar claims to have had "many adventures" on his way back to Omaha from Oz, yet we never learn what they are. I've had a story planned about this very subject for years, but I've only managed to write a few pages so far.