A lot of adventures begin with the premise that the party members are just average commoners, minding their own business, until events of the plot drive them to heroism. What could be better for demonstrating the hero's journey than starting from nothing, and shaping one's own destiny into legendary form? In spite of this plot's popularity, it's actually extremely difficult to do in D&D.
In 5th edition, even a first level character is assumed to have heroic predispositions. Fighters are exceptional in their fighting skills, rogues are exceptional thieves, and clerics are exceptional priests. It is impossible in the core rules to play an everyday schmuck player character. So, I'll quickly present some rules if you want to start your campaign from level zero.
Your character has no class levels, no background, and no proficiency bonus. Just as well, because you don't have any proficiencies either. You have your six ability scores, and a d20 to roll. You hit points are equal to 1d4 + your Constitution modifier (minimum 1). May luck be on your side.
Your adventurer doesn't deserve the title yet. He might be qualified to defend a household, but not a village or a city. Your greatest challenge may be a bloodthirsty goblin or a hungry wolf.
If you miraculously survive level 0, you can level up to level 0.5. You gain a background, a proficiency bonus of +1, and proficiency with one weapon, skill, or tool set. Your hit points go up by 1.
Your adventurer has gained some notoriety, at least in a small town, and has become a little bolder as a result. You might even go toe-to-toe with another commoner, if things don't go your way.
When the time comes to level up to level 1, your proficiency bonus increases to +2, and you keep your additional skill, tool, or weapon proficiency (you’ve earned it.) You finally get a class level, and everything that comes with it.
You're a fully-fledged adventurer, remarkable compared to every other commoner, with a life of excitement and danger ahead of you. Now go fight Demogorgon!
Changelog: 8/10/16: HP Level 0: Should have been 1d4