How would you go about making this guy? 

*warning blood*

https://www.youtube.com/watch?v=doVYFjIJcfU

I forgot how much fun that movie was :)

I'd go Ranger (Hunter) with two weapon fighting option; take Hoard Breaker for up to four thrown knives per round.

You can only draw one weapon a round. If you have the Dual Wielder feat, you can draw two. If you want to throw 4, you need to start combat with two in hand and draw two that round.

Hoard breaker doesn't work anyway because it requires the "same" weapon.

I would go Barbarian and take the Dual Wielder feat.

I'd allow it as DM. Its only a minor tweak to allow a concept to function.  Right now, there's nothing to really allow thrown weapons to work in this way, so you're going to need DM-ness to let it work in the first place.  

I mean, you could also just accept that you won't be getting multiple knife throws in a single turn and go Swashbuckler.

Monks are pretty good with darts and daggers, since they can use their monk damage die for them instead of their crappy d4's. 

The problem with monks is that they're restricted to only two knife/dart attacks per turn; you'll definitely need the Dual Wielding feat just to do the drawing, and you'll never get the +STR/+DEX damage bonus for any bonus action attack, which renders the increased damage die moot. Any bonus action attack, or Flurry of Blows, must use the unarmed strike. Most subclasses either have their own innate ranged attacks or have abilities that rely on melee attacks (of which knife throwing is not one).  Swordsaint is the only subclass that might work, and that's if you stick to throwing range, ignore the level 11 feature, and never pick up a longbow which is a more effective weapon.

One of my biggest complaints in 5th is the loss of the thrower build.

I loved the dart/dagger fighter in 2nd Ed, and they were pretty good in 3rd until the monsters had DR.

5e just makes them impossible as anything but an minor thing.

If you forgo daggers in favor of darts, they at least count as ranged weapons, which means they can benefit from things like the Sharpshooter feat and archery fighting style. I'm not sure what's else to add so that's not quite a build, but more of a gimmick.

Something else to potentially consider is that if throwing stuff is the only goal, then there's probably something that can be done with magic stone.

Not sure how it would fit into any sort of optimization, but being an Eldritch Knight gives you a way to throw three or even four daggers if you have the attacks, since you can summon a bonded dagger using your bonus action, which isn't the same as the two free draws you get per round with dual wielder. 

If you start combat with two daggers drawn (one of which is your bound weapon), you can throw both, draw two more for free, throw those two, and then summon the bound one back with your bonus for four attacks total leaving you with one dagger in one hand at the end of the round. Then on the next round, another four attacks: throw dagger, draw dagger free, throw dagger, draw dagger free, throw dagger, bonus action summon special dagger, throw special dagger, leaving you empty handed. Then on the third and subsequent rounds, only three attacks: draw two daggers free, throw both, bonus action summon, throw dagger, leaving you empty handed, etc etc. 

I dunno about daggers and darts... but that actually sounds like a pretty cool Eldritch Javelin or Throwing Axe build, I might do that some time :)

Archery Fighting Style gives you bonus with any ranged so that would work.

Well I only watched like the first 20-30 episodes of Critical Role's first campaign but didn't Vax have a special belt that allowed his knives to teleport to him after he'd thrown them? 

Even if the character did, that's stepping into custom magic item territory. That's going to depend on your individual DM

Javelin of Backbiting already has a relevant ability, and reskinning a magic item from one base item to another might be viewed as a little less homebrew-y than writing one up from scratch.

Darts reskinned as throwing knives (As someone who owns throwing knives and practices with them occasionally, a dagger and throwing knife are extremely different. Throwing knives are often designed to stack where daggers aren't. Go monk for higher damage, sharpshooter feat. A few levels of fighter for archery fighting style and action surge.

way of kensai to make darts count as monk weapons for all their lovely perks.

I built a very basic version without magical items targeted at level 20

https://www.dndbeyond.com/profile/Pseudoimmortal/characters/4308808

BA: add 1d4 to all attacks on the same turn. 4 darts per turn with action surge. 2 other wise so 2x 1d10+5 +1d4. 7-19 damage per dart, 14-38 damage per average turn, 28-76 on action surge. The numbers are a little weak but monks aren't powerhouses. If you dropped monk down to 4 and took something like barbarian, you could keep kensai shot and get bonus damage for rage.

Oooor, you could do something like reskin sun monk as weapon based if you wanted but that's....iffy I suppose.

Darts don't have the "ammunition" property, so you can't throw as many as you want.  Just like with daggers they have to be draw and thrown.

Quote from Jiracorp626 >>

Well I only watched like the first 20-30 episodes of Critical Role's first campaign but didn't Vax have a special belt that allowed his knives to teleport to him after he'd thrown them? 

 Yes, its called a "Blink Back Belt". Its a Pathfinder game item they kept when they converted over to D&D 5E at the beginning of their streaming.

Okay real talk... fiddled with Eldritch Knight thrower a little bit, and he can make darts pretty scary! Its not to say that everything he does couldn't be done better with a real ranged weapon (except maybe slightly better AC), but its not that bad if you're more into the concept than optimization. 'll talk about the level 20 build, but really a dart thrower can get pretty effective at low levels just with sharpshooter and a decent dex.

Eldritch Knight 12/Hexblade (Pact of Blade) 8
Build for 20 Dex (or Str), 20 Con, whatever else because no more than 13 Charisma is needed.
Feats: Sharpshooter, Dual Wielder, Martial Adept
Race: Human gets you feats quicker and on track for 20 Dex/20 Con, but no real racial requirements. 
Invocations taken: Devil Sight, Armor of Shadows, Improved Pact Weapon, Eldritch Smite

Benefits:

- 3 attacks per attack action, which is the maximum number of sustainable thrown attacks per round anyway (2 free draws, and one summoned to hand as a bonus action)
- 1d4+15 per dart using sharpshooter. Add +6 if you've hexblade cursed a target, +1d6 if it's Hexed (cast it with an Eldritch slot, save the warlock slots), +5d8 and prone if you burn a warlock spell slot as part of the attack. So average hits of 49.5 for the first two darts if you're pulling out all the stops in an alpha strike, followed by 27 per dart for the rest of the fight.
- If you're just shy of hitting with a sharpshooter throw, you can try to make it hit with a 1d6 precision attack martial adept die roll. Or, if something big and nasty looks like it wants to run at you, buy yourself a round by frightening it with a DC 19 menacing attack that adds a couple more points of damage.
- Spells, spells, spells. You aren't taking anything with a saving throw under Eldritch Knight or Warlock, so you're loaded up with juicy utility spells like Fly, Darkness, and Shield that make you better at throwing daggers or staying alive, without forcing you to stop throwing. Whenever possible, try casting with Eldritch slots, so you can save the warlock slots for smiting.
- You'll probably be burning through too many darts to enchant them all,  but you can invest in at least one or two nice ones that are bound as your Eldritch Knight bonded weapons, and get a free +1 magic dart via Improved Pact Weapon.  
- Great HP (216 at 20), and pretty decent AC. 18 normally with your mage armor (or plate, if Str based). Can be 20 if you carry around a shield in your off hand, because it doesn't slow down how many darts you can draw or throw, and you aren't going to benefit from dual wielder's AC bonus anyway because darts aren't melee weapons. And you can always use Shield (the spell) as a reaction for another 5, bumping you up to 25. 
- You can pick up a poisonous snake familiar if you'd like, and dabble with poisoning some darts if your DM is ammenable. 2-5 damage isn't much end game, but could be fun to play around with when it first comes up at Fighter 3. 
- Pretty hard for the DM to take you "out of your element." You've got two different ways to summon a total of 3 darts from anywhere, even if you're disarmed. You've got mage armor at will (if you're Dex based), so you can't really be stripped naked (though he can steal your cheezy offhand shield). You can attack without disadvantage from melee all the way out to 60 feet, which covers most combat scenarios, and have the darkvision to match. 
-Action surge is always fun. Won't really help you throw more daggers, but could be useful for getting some buff spells up in the first round of combat. 
-SAD as hell. 20 Dex and 13 charisma is all you actually care about, the 20 con is just the most sensible thing to do with the rest of your points and ASI. If you're rolling for stats in a game and don't do so hot, it's a pretty fun build to be able to pull out of your back pocket with a single 15 if everything else is garbage. Or, you can just grab a bunch of fluff feats! Or, you can even run it as Strength based if you feel like it, since Darts are finesse and give you the choice, and wear plate armor for the same base 18 AC. 

As a DM I would allow a character to stack two throwing knives in one hand. However, as someone else noted throwers are NOT daggers so I would count them as darts (so you can't use them in melee at all). I would allow you to throw both at a single target with no penalty or at two targets for a -5 to each. With Two-Weapon Fighting you get your modifiers with the second attack and you'll need multiple Attacks (of course). So, here's how I would do it:

At level 5 a Fighter has access to 2 Attacks, the Two-Weapon Fighting Style, Action Surge and a Feat if you're a Human Variant.

A combat would see you starting with 4 darts (throwing knives) in-hand.

Your action would be to make 2 Attacks with a total of 4 darts, take a Bonus action to draw 2 more, Action Surge and then throw the two you just drew. Of course, you can move during all of this as you choose. That's 6 darts in a round but since you burned the Action Surge you only get 2 darts next turn unless the DM will allow you to draw 4 instead of 2.