Jabes.plays.RPG says:
Anyone can wield two weapons and attack twice on their turn as long as both weapons are light, one-handed melee weapons. You use your Action for the main attack, and a Bonus Action for the "off-hand" attack. It's a little more involved than that; we can get into it if you're interested.
Demagor says:
...how does one roll/calculate to-hit odds when attacking with two weapons?
Two-weapon Fighting in D&D 5e
ANYONE can wield two weapons and attack twice as long as both weapons are light, one-handed melee weapons. You spend your Action for the main attack, and your Bonus Action for the "off-hand" attack. This assumes you have not already used your Bonus Action this round for something else. You still add your attack bonus (ability modifier+proficiency bonus) to the off-hand attack roll, but you do NOT add your ability modifier to the off-hand attack's damage.
With the
Two-Weapon Fighting Style, you get to add your ability modifier to the off-hand attack.
With an
Action Surge, a Fighter can take an extra Action, which they can use to attack once more. This is considered a "main-hand" attack, so the ability modifier is added to the damage.
At 4th level, you get access to feats. With the
Dual Wielder feat, you are no longer restricted to light weapons. And you can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.
At 5th level, some classes gain the
Extra Attack feature. With a single Action, you can attack twice (both considered main-hand attack)! So a dual-wielding fighter can main-hand attack twice with their Action, main-hand attack another two times with an Action Surge, and off-hand attack once with their Bonus action!
Read more about TWF
here and
here.
Dual-wielding with one or both weapons non-light.
First of all, it is perfectly legal to wield that combo as long as you don't actually attempt to attack with both weapons in a turn. You can attack with the longsword this turn, then attack with the handaxe next turn. When you get the Extra Attack feature, it doesn't matter which weapon you choose to attack with for your Attack Action. It only matters when you try to use the Bonus Action to get an extra off-hand attack.
Okay, so you want to use the Bonus action to get an extra off-hand attack. If we follow RAW (Rules As Written), in other words, follow the rules to the letter, the answer is,
"You can't. Unless you learn the Dual Wielder feat." but many DMs will have their own houserules for this. I'll leave it up to Len to say what goes here in this particular game.