How did DC Comics reboot Superman in 1986?

Question

According to Wikipedia:

The Man of Steel is a 1986 comic book limited series featuring the DC Comics character Superman. Written and drawn by John Byrne, the series was presented in six issues which were inked by Dick Giordano. The series told the story of Superman's modern origin, which had been rebooted following the 1986 series Crisis on Infinite Earths.

How did they reboot the character? Have they had him killed in the crisis then came up with a story to bring him back? Or the case of readers waking up in 1986 to find out the next issue was simply talking about a totally different version of superman?

Answer 1

tl;dr: It was actually a combination of both. Before Crisis on Infinite Earths there were two Superman characters. Afterward, one has died and the history of the other had been rewritten. Man of Steel tells the new story as it was post-Crisis.

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The Crisis on Infinite Earths storyline was an incredibly complex mess, meant to clean up the even bigger mess that had been made of DC's continuity at that point. Over the decades, Superman's backstory and powers had been constantly changed and evolved (he originally couldn't fly; he was originally the only Kryptonian but later found Supergirl, etc.)

By the time of the crisis event, there were already two Superman characters in DC history. The first was "Kal-L" from the Golden Age, the original Superman from 1938. The other was "Kal-El" from the Silver Age, who was introduced as Superboy in 1945. When Superboy's backstory conflicted with Kal-L's backstory, DC introduced the concept of the "multiverse" to explain these different versions of the characters -- young Kal-El (from "Earth-One") even meets young Kal-L (from "Earth-Two") at one point and trains him.

On top of that, most of the other DC characters had run into similar problems, with two (or more) versions of the same character appearing in different versions of Earth, sometimes crossing over to interact with each other. This got too confusing for anyone to follow, and if you were trying to read multiple series with the same characters, it was a big headache. So, DC came up with the Crisis.

During the Crisis, a super-powerful multi-dimensional being started messing around with the multi-verse. All the heroes from Earth-One and Earth-Two came together to fight him. In the end, the older Earth-Two Superman sacrificed his life, and Kal-El from Earth-One was left alive. All the different Earths were merged together into a single universe, and everyone's backstories have been rewritten into new versions of the character.

Man of Steel lays out the new, revised, post-Crisis version of Superman's origin.

Answer 2

As mentioned in the Wikipedia article you quote, the reboot was in the wake of Crisis on Infinite Earths wherein

The conflicting origins and stories of the DC universe are explained as a Multiverse, containing many parallel universes and alternate versions of the characters, with the primary DC continuity referred to as Earth-1.

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A cosmically empowered Anti-Monitor attacks again, transporting the new Earth to the antimatter universe and summoning a horde of shadow demons. He falls in a carefully planned counterattack culminating in a battle with Kal-L (the Earth-Two Superman), Alexander Luthor of Earth-Three and Superboy of Earth-Prime, with help from New Gods adversary Darkseid. In this final battle the Anti-Monitor, reduced to a flaming head, crashes into a star and is killed by the Earth-Two Superman. As they are the only four who remember the original past, Alex sends Earth-Two Superman, Earth-Two Lois Lane, Earth-Prime Superboy and himself to a pocket "paradise" dimension.

So, in short, part of the purpose of the book was to say "all of these contradictory backstories are because there are multiple universes that are very similar, but not quite alike. Afterwards, with all of the realities merged, DC could state the "true" backstory as being the case.

As regards killing off Superman, that actually was one of the plans:

According to George Pérez in a Wizard magazine interview in 1994, Chris Claremont suggested that Superman of Earth-One dies in the final battle with the Anti-Monitor in issue #12. After the Anti-Monitor was destroyed for good, Kal-L from Earth-Two realizes that he is now alone, without his Earth, without his Lois, and now the new single Earth is without a Superman. Then he remarks, "Don't need this anymore," and brushes the white dye off his hair and other make-up that he apparently used to make himself look aged. The other heroes are surprised by this and Kal-L simply explains that he had stopped aging when he reached the peak of his powers. He returns with the other heroes to the new post-Crisis Earth, taking the place of the Earth-One Superman.

If this idea had been used, then The Man of Steel would have marked the return of the "Original Super-Hero", as Kal-L (now switched to Kal-El) begins his life on the post-Crisis Earth, which is similar to his old life, but with distinct differences. Despite this "culture shock," Kal-L endures and is given a new lease on life by being deposited back to the early days of the modern heroic age of the post-Crisis Earth. However, this was discarded when the John Byrne version of The Man of Steel was planned.