The movie shows Lex Luthor mixing his own blood with that of General Zod to create the monster in the Genesis Chamber of the Kryptonian spaceship that crashed in Man of Steel.
For those who skipped Man of Steel, the Genesis Chamber is used to create beings. By destroying the ship in Man of Steel, Superman (presumably) throws away any chance he had of creating more of his race.
Given the damage to that ship, it’s unclear how Doomsday is created. The Kryptonian science behind General Zod’s transformation goes largely unexplained in Batman v Superman.