Say I have a fighter who has three attacks and uses ready action/hold action to "Attack the next person to come through that door". If someone comes through the door, does he get his reaction to get three attacks then on his regular initiative when his turn comes around make his normal three attacks for that round as well?
You get one attack from a Readied Attack action
Based on Jeremy Crawford's ruling:
@JeremyECrawford. A player with multi attack readies an attack, do they get all attacks on the trigger or just one
Jeremy Crawford @JeremyECrawford
@Koontz If you mean the Extra Attack feature, the extra attacks happen only on your turn.
This is because Extra Attacks need you to:
Use the Attack action
Do it on your turn
When you ready an attack, you are:
Using the Ready action
Attacking outside your turn
And so Extra Attack doesn't apply, and you only get one attack.