I am getting ready to play D&D for the first time and really excited! I have been watching Critical Role to learn a little more. I am going to be playing a rogue and on Critical Role Vax often attacks with 3 daggers. When you're duel wielding do both attacks count as one then using a bonus action to get to third? It has been confusing me.
You're rightly confused — you don't normally get three attacks per round like that. By itself, fighting with two weapons gives you at most two attacks — one from the normal Attack Action and one from a Bonus Action with the off-hand weapon.
Vax therefore has something else going on that is allowing that third attack. From the Critical Role Wiki's FAQ:
How does Vax get 3 attacks per round?
He dual wields daggers for 2 attacks and has a custom magic item brought over from Pathfinder called boots of haste which function like the spell.
So Vax is making the first two attacks according to the normal rules for Two-Weapon Fighting (on page 195 of the PHB), and then making a third via the extra Action granted by D&D 5e's version of the spell haste (p. 250).