It says in the Two-Weapon Fighting attack option (PHB, 165):
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.
And then there is the Dual Wielder feat in the PHB:
You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.
It somehow gave me an impression that I now may be able to do two attacks in one action, and then the next two as the bonus action, since it says that my weapon productivity literally doubles? Or else, what use can be made out of this addition to the feature?
I also chose the Two-Weapon Fighting fighting style as a Fighter class option, and at that point I am interested only in whether any of these provide me with the right to stab people four times per turn or not.
How many attacks exactly do I get if I combine the Dual Wielder feat with the Two-Weapon Fighting fighting style?
Best Answer
You can take the Attack action once and make another attack as a bonus action.
(Note the uppercase-A vs. lowercase-a attacks, there.)
You can take the Attack action, as one does. Per "Two-Weapon Fighting" (PHB 195) when anyone does that with a light, one-handed weapon they can make a second attack as a bonus action with another light, one-handed weapon in the other hand.
Dual wielder, in the second bullet, basically just erases the word "light" from the two-weapon fighting rule to make it:
So now you can wade into battle with two battleaxes, rather than two handaxes.
Two-Weapon Fighting style adds a modifier to the bonus action attack.
Neither Dual Weilder nor the fighting style change the number of attacks, though: you're still limited to whatever's provided by your Attack action plus one bonus-action attack.
If you want to stab someone four times (and, really, who hasn't been there?) look additionally toward Extra Attack, Action Surge, haste... those cover 99% of the ways you could get to a 4th attack.