The Beyonder first "appeared" as a disembodied voice in Secret Wars #1. He teleported several heroes and villains into space, declaring that the side that won would "have their greatest desire fulfilled", then destroyed a sector of a solar system and reformed it into Battleworld. Doctor Doom found a way to siphon Beyonder's power into himself, but was tricked into relinquishing it, but eventually found a way back to Earth with the help of Molecule Man, whom Doom helped to release his full potential as the most powerful metahuman in the Marvel universe
However, a few months later, the Beyonder showed up on Molecule Man's doorstep, wishing to know more about humanity and desire. MM told him to go out there and experience life in order to understand the nature of desire. See, the same accident that gave MM his powers also opened a "pinhole" into the dimension that the Beyonder lived in. Actually, Beyonder WAS the dimension. Everything that existed in there was just his vast energies and nothing else. Once the pinhole opened, he could see how "incomplete" humans were and the desire that comes from this. As a result, the Beyonder also began to feel incompleteness and desire, previously thinking he was complete due to being all that was in his dimension. Hence, his "Secret War" was an attempt to fully understand desire.
This resulted in the Beyonder taking various human forms before finally settling on one based on Captain America with slight alterations in hair color and style. In his travels, he empowered a writer who went amok, turned a building to gold after Luke Cage explained the value of money, had Spider-Man showing him how to take a dump (no, seriously), started a life-improvement cult, became a pro wrestler, became a superhero, was taken under the wing of a gangster who treated him to a gang bang with several hookers, fell in love with Dazzler but was rebuffed, killed and revived Death herself, and eventually got so frustrated with humanity and the lack of his desires being fulfilled that he went nuts and slaughtered the New Mutants.
His killing of Death earned the ire of the greater powers in the MCU, especially Mephisto; for if Death did not exist, then no one can die and there are no souls to collect. Despite a failed attempt that almost destroyed half of the universe, Misty wasn't done with the Beyonder. Beyonder then decided that he couldn't beat them, so he would join them, and thus sought to become reborn as a human. Since being born "the old fashioned way" would be too time consuming and messy (as he put it), he built a machine and tested it by resurrecting the New Mutants. Then he used the machine and became an ordinary human, but he freaked out and reclaimed his powers from the machine. However, he realized that he desired humanity too much and tried again, this time relishing having limits like getting winded from running and unable to lift anything heavy. Then Mephisto came calling at his most vulnerable, but Beyonder was able to reclaim his power and scare Misty away.
So Beyonder realized he needed to revise his plan lest his enemies kill him. He was now going to be reborn as a human, but then have the machine feed his power in his developing new body, making him a human but with his power intact. This is when Molecule Man and every MCU hero struck, resulting in a battle that literally cut a scar across the universe, and MM used his power to TELEPORT EVERY LIVING THING OUT OF THE WAY of the Beyonder's attack, but it still incapacitated the heroes long enough for Beyonder to start the machine's process. However, before it could be completed, MM defeated the fail safes and destroyed the machine, killing the Beyonder while it was still a fetus. His energies were rerouted back into his dimension or else it would have destroyed everything, resulting in the creation of the New Universe. The aftermath resulted in the Earth nearly breaking in half, but MM combining his power with the Silver Surfer repaired everything, with MM faking a loss of his powers so he and his girlfriend could live in peace like he did before Beyonder showed up.
BUT WAIT! THERE'S MORE! A few years later, it was revealed that the Beyonder reformed into his own reality, and was actually an immature Cosmic Cube, which are essentially "eggs" for the energies of a race called the Beyonders. Part of his energies "escaped" his incubation dimension during the accident that gave Molecule Man his powers, thus leaving Beyonder ( a "child" compared to the Beyonders) incomplete and unstable since there was no Cosmic Cube to act as an "egg" and finish developing correctly. So with the help of another entity that developed from a Cosmic Cube, Beyonder and Molecule Man merged to become a complete entity and left to learn more.
Then the combined entity came back later, "spit out" Molecule Man, and became an insane woman named The Maker for some reason. The End. Also, then Bendis decided to be a r3tard and explain that the Beyonder was "really" an insane Mutant Inhuman (hence his godly powers), but everyone chose to ignore this because it was stupid and made no sense.
Oh, and the Beyonder race, so powerful that they could not exist in our reality, finally reared their freaky alien heads and almost destroyed EVERY reality in the MCU, resulting in the 2015 Secret Wars saga.