There are three things in the rules that I’m aware of that talk about fighting with two weapons:
There is a subsection in the basic rules called Two-Weapon Fighting. These are the base rules for anyone using two weapons (BA attack without ability modifier, must use light weapons)
There is also a fighting style called Two-Weapon Fighting available to fighters and a couple of specific subclasses (Swashbuckler has that option, I think). This fighting style allows you to add your ability modifier to the off-hand attack.
There is a feat called Dual Wielding (Player’s Handbook) that grants additional bonuses: the weapons don’t have to be light, a +1 AC bonus, and you’re able to draw or stow both weapons at once.
Not completely right
(5.5e) Two-weapon fighting is a Fighting Style that only some classes can get.
Dual Wielder is a general Feat that any character of level 4 with str or dex 13 or higher can take.
Anyone can dual wield when their main weapon has the Light property.
There are three things in the rules that I’m aware of that talk about fighting with two weapons: