In PHB weapons are declared wielded, but no clarification is made that one hand is main and the other is off-hand.
This has a few implications. Say a character rogue is holding a dagger and a club and fighting foes weak to bludgeoning. Upon declaring the attack action the player must... choose with which weapon to attack. After that attack hits or misses, the player can choose to use Two-Weapon Fighting to attack with the other, or use any other bonus action.
At level 5 when extra attack enters the mix things get interesting. Now Extra Attack allows you to use the attack action to attack with the same weapon twice, or each weapon once. Doing this opens the bonus action to use either weapon.
On Rogue > Sneak attack
Sneak attack in 5e is not an action but rather a rider on every attack. this is important as a thief dual wielding should be able to land a sneak attack on an attack made with the Two-Weapon Fighting bonus action if they were to miss with the Attack Action.
On Rogue > Thief > Fast Hands / Potion of speed / Haste?
Thief's should not have a second bonus action. this entirely changes the feel of the class. In D&D 5e they have another option to use their bonus action not a second one. The bonus action is highly valued and while fighters can get a second action (action surge) there are no ways to get a second bonus action.
On Rogue > Cunning Action / Hide Hide is an action not a bonus action.