All use of Inspiration should be narrated in gameplay.
Start the game with one inspiration. Players may have inspiration up to their proficiency bonus.
How to Gain Inspiration
DM decides to grant inspiration (usually for outstanding role play).
Players all agree to grant a player inspiration for outstanding role play in conjunction with Background, Alignment, Personality Traits, or Ideals, Bonds, or Flaws.
Player of a character who goes unconscious can grant another player's character inspiration (if they had any). The idea being that seeing their friend in trouble spurs the rest of the party to fight harder.
DM can bribe a player into accepting a complication based on Background, Alignment, Personality Traits, or Ideals, Bonds, or Flaws. (since you hate nobles, wouldn't you...)
How to Spend Inspiration
Can only spend one Inspiration at a time.
Re-roll a failed dice roll, or gain a plus +5 (attacks, saves, skill checks).
Re-roll any single die. (including damage or maneuver die, etc).
Automatic success on a death save (decide before roll).