When you start your turn with 0 hit points, you must make a DC 10 saving throw to determine whether you creep closer to death or hang onto life.
Roll a d20. 10 or higher = success. Below 10 = failure. Rolling a 1 counts as two failures. Rolling a 20 = regain 1 HP.
Three successes: You become stable (unconscious but not dying).
Three failures: You die.
Taking damage at 0 HP = one failed death save. A critical hit = two failures.