These rules are adapted from those appearing in D&D Player’s Basic Rules v0.2 — Chapter 9: Combat and the modified 2nd edition rules appearing on Injury and Death.

Dropping to 0 Hit Points
When you drop to 0 hit points, you either die outright or fall unconscious, as explained in the following sections.

Instant Death
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.

For example, Grond, who has a maximum of 9 hit points, currently has 7 hit points. If he takes at least 16 damage from a single attack, he is reduced to 0 hit points, but 9 damage remains. Because the remaining damage equals (or exceeds) his hit point maximum, the Grond dies.

Falling “Unconscious”
If damage reduces you to 0 hit points and fails to kill you, your character falls prone, incapacitated and barely conscious (which shall hereafter be referred to as “unconscious”).

An unconscious creature is incapacitated (see the condition in appendix A), can’t move, and can not take any action or reaction. He remains aware of his surroundings, can speak, quietly (usually to croak “help”, recite some soon-to-be-famous last words, offer advice to allies, or quote some Monty Python “I’m not dead yet…”), but can take no other actions (even purely mental ones). The creature drops whatever it’s holding, automatically fails Strength and Dexterity saving throws, and all attack rolls against the creature have advantage.

Death Saving Throws
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn’t tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.

Roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail. A success or failure has no effect by itself. On your third success, you become stable (see below). On your third failure, you die. The successes and failures don’t need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you regain any hit points or become stable.

Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. If you roll a 20 on the d20, you immediately regain 1 hit point.

Damage at 0 Hit Points:
If you take any damage while you have 0 hit points, you automatically suffer a specific injury (see Critical Hits). This is rolled as a normal critical hit (d10 for location, base damage die for severity). If the damage is from a critical hit, the attacker uses the doubled damage dice to determine the severity of the injury (thus a critical hit with a one-handed longsword against a character at 0 hit points has a severity of 2d8, and thus is probably cutting your head off). If the damage from the attack exceeds your hit point maximum, you suffer instant death (in addition to the maiming, which may make it harder to raise or otherwise resuscitate you).

These attacks have no effect on the count of your Death Saving Throws.

Stabilizing a Creature
The best way to save a creature with 0 hit points is to heal it. If healing is unavailable, the creature can at least be stabilized so that it isn’t killed by a failed death saving throw.

You can use your action to administer first aid to an unconscious creature and attempt to stabilize it, which requires a successful DC 10 Wisdom (Medicine) check. A stable creature doesn’t make death saving throws, even though it has 0 hit points, but it does remain unconscious. The creature stops being stable, and must start making death saving throws again, if it takes any damage. A stable creature that isn’t healed regains 1 hit point after 1d4 hours.

Monsters and NPCs and Death:
Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

Mighty villains and special nonplayer characters are common exceptions; the DM might have them fall unconscious and follow the same rules as player characters.

PCs are free (and encouraged) to hack up the bodies all they want.