Minor Gods are just above mortals. They're nothing but mortals with enough power to instantly teleport or fly. They may have other abilities, but those are the defining traits.
There are many ways to reach this point. As a Human, knowledge can be the thing that tips the scale between Godhood and mortality. For Demons, stealing Souls is their way to Godhood, but many never reach that point. For less intelligent races, or those who are generally weak, their power comes from the equipment they wear. It is also possible to become a God with another God's help. Gods can transfer power to others by attacking someone, and they absorb it. Or, a safer way is if the God gives the mortal a Meganova Gem, and the mortal drains the Mana into themselves. If the mortal survives the sheer force of the Gem, they then become a God.
Minor Gods rarely reach the status of Lesser God, because at this level, they aren't fully immortal. Most Minor Gods can be killed by conventional means. Some others require rituals to be weakened, then killed.