Buy Superman Doomsday Comics
Starting in 1992's Superman: The Man of Steel #17, the final page of each title showed a gloved fist bursting metal cables and relentlessly pounding on a metal wall with the tag line, "...Doomsday is coming!" until the hooded figure finally broke free from it's underground prison.
In Superman: The Man of Steel #18, writer Louise Simonson (with penciller Jon Bogdanove and inker Dennis Janke), avoiding subtlety in her effort to convince readers about the evil nature of the newest villain, has Doomsday extend a hand for a cute little birdie to land. Only to have Doomsday crush it with a blood red "BLORCH" sound effect accompanied by stereotypical bad guy laughter, "HAH ... HA HA HAAA".
Okay, character established.
While Superman is busy with other matters, the monster begins his rampage across pastures and roadways, leaving destruction in his wake (and continuing the maniacal laughter).
The JLA intervenes in Justice League of America #69, (story/art by Dan Jurgens with finished art by Rick Burchett) but the team is quickly decimated. At the issue's end, Superman saves Booster Gold who says, "it's like doomsday is here!".
Superman gets a personal introduction to the beast in Superman #74 (story/art Dan Jurgens with finished art by Brett Breeding) and is battered around. The combined efforts of Superman and the JLA serve only to tear off Doomsday's container suit, exposing massive muscles and bony protrusions topped by nasty face with blood-red eyes.
Superman and the JLA continue the battle in The Adventures of Superman #497 (Jerry Ordway writing with Tom Grummett penciling and Doug Hazlewood inking). Spotting a giant television advertising a WWF type wrestling event in Metropolis, Doomsday begins growling "Mhh-trr-plss" and begins heading to town. Superman is left to fight alone in Action Comics #684 (Roger Stern writing with the artist team of Jackson Guice and Dennis Rodier) and Superman: The Man of Steel #19, despite the brief efforts of the Guardian and Supergirl as Doomsday continues his devastating advance.
Finally, in Superman #75, Superman and Doomsday (in a series of spectacular full page illustrations by Jurgens & Breeding) strike simultaneous, apparently fatal, blows - leaving two bodies amidst the rubble of Metropolis (all of the above stories are collected in the trade paperback, The Death of Superman.
Cadmus Labs takes charge of Doomsday's body while the world mourns Superman in the excellent "Funeral For A Friend" story arc (collected in the trade paperback of the same name). Then in Superman #78, the Cyborg version of Superman breaks into Cadmus and flies into space with Doomsday's body - using metal cables to bind it to an asteroid and then tossing the asteroid off into deep space to "float forever ... buried in the infinite void".
The final page of that issue shows the monster alive, awake and laughing as his asteroid tumbles off into the darkness.