As you all know, battles are things which occur in wars. However, I am wondering how to play out such a battle with PCs. Basically, I want my BBEG to bring his forces against the combined effort of humanity, with my players being on humanities side. There will be some tactics, like to separate the BBEG from his army, and the BBEG's army will use acid canons to get rid of high ranking mages, but I want to know how to run all this with my players. How do I determine how combat plays out when there us a sea of enemies already battling an army? How can my players feel impactful in a battle between hard hitters, in a battle between armies?

The PCs should not be in the front line slugging it out with the troops. They get the special missions. Maybe they get sent to destroy those acid cannons you mentioned. Or need to find a way to get behind the lines and do … something. Maybe it’s find and kill the BBEG, but maybe there’s other strategic options. Like they need to destroy a bridge (or valley or road or other position) the enemies are using for supplies and reserve troops, or of not destroy, take control of it and hold it until reinforcements arrive. Or scout the enemy locations. Or destroy a fortification. 
Ideally, you give them multiple targets where they can’t possibly do all of them, so they need to decide which they think are most important. Oh, and part way through, they hear that a favorite NPC’s position is being overrun, so do they save their friend or keep fighting in other areas.

Then you factor their actions into the overall battle. I usually think of it like, if the PCs aren’t there, the bad guys will win. Then from there you figure they achieved goals A and D, but not B or C, so what does that mean. 
And leave open the possibility that the overall battle ends in a draw. Or at least that the fighting is inconclusive after one day. Then they regroup and see what options they have for the next day.

The short answer is: this scenario really doesn't work very well in D&D.

Unless the main enemy is somehow magically supporting their forces (and this was well-established beforehand, so it doesn't feel like a cop-out), the best justification I can come up with is that taking down the main boss will break their army's morale.

My suggestion is to treat the entire large battle as metaphor: get the PCs into a fight with the main boss, and just describe the ebb and flow of the larger battle in direct correspondence with the ebb and flow of the boss fight. A PC lands a hit, and the elven cavalry crashes into the orcish lines. The wizard takes a big hit, and fire rains down upon the good guys' artillery.

I agree with Xalthu, if you stick your players on the front line it’ll just be a long slog of them killing endless mooks without ever feeling like they’re winning so instead treat them like Special Forces and give them objectives that will decide the fate of the battle separate from the main fight. Taking out siege weapons, assassinating generals, disrupting supply lines or destroying routes to the battle are all things that can keep them occupied in the smaller fights D&D is designed for and make them feel like they’re accomplishing something tangible. A lot can even be done in advance of the fight starting and instead of you having to micromanage an army you can instead narrate how a regiment collapses without their leader, how fighters run out of arrows because the wagon with equipment never made it there or how reinforcements never arrived because a bridge had been destroyed 

In this situation (particularly as a climactic moment for a long campaign; what I'm about to suggest is a little overcomplicated to make a habit of), I might consider doing something like putting the players in charge of an elite reserve unit or something like that. Then work out a few decision points where there are multiple "hotspots" in the battle that they have to prioritize. Like, maybe the enemy is breaking through the good guys' lines in one place, but there's another where team good guy has an advantage that could be decisive if pressed, so they have to choose between the cautious or aggressive approach. When they actually get there, their personal part is mostly just a fight against some elite soldiers from the opposing side, and when it's over you talk some more about the larger battle to give them a sense of whether they made a good call or not. If you break it up into explicit decision points, you probably don't need too many of them by the time it all plays out. Maybe just three or four that the players actually see, plus some alternative scenarios depending on whether the battle's going well or poorly, and you can reuse the same personal fights across multiple mutually exclusive scenarios to mitigate prep work.

But something like that to give them a taste of the tactical level without either leaving the whole battle out of their control or needing actual mass combat mechanics.

Alright, I can see how I could have them take out some acid canons, go to take out a general, sabatoge supplies, distract the BBEG, or do some other plan in war other than endlessly fighting, but how do I implement those in the heat of a massive battle? It's rather hard to fight a Commander or take out a seige weapon while they're in the middle of a large army.

Quote from Elgoblino10986 >>

Alright, I can see how I could have them take out some acid canons, go to take out a general, sabatoge supplies, distract the BBEG, or do some other plan in war other than endlessly fighting, but how do I implement those in the heat of a massive battle? It's rather hard to fight a Commander or take out a seige weapon while they're in the middle of a large army.

 Have them operate behind the lines. The vast majority of the troops are fighting up front, leaving relatively small numbers defending the artillery and command posts.

Also, just assume the nobody foot soldiers in the area will break and run when the PCs effortlessly cut down the first few. (Don't even roll that bit out, just specify that it happens.) Only the elite guards and major NPCs will stand and fight, leaving you with a manageable fight.

Them being more behind the lines is a good idea, I could set up some battles with reinforcements as the go around the main front line to reach the commanders/weapons or whatever. 

Well, I think I got enough advice to run this effectively, I'd like to thank you all for helping me.

How they do it is their problem. You just decide where the stuff is. It’s up to them how they get to it. Getting to the rear ends up being part of the challenge. Do they go around, try to sneak through either with stealth or a disguise, look for a weak point and try to cut their way through? It’s up to them. They have powers and magic items they can use, NPCs who owe them a favor, gold to bribe people, etc.

Also, generals rarely if ever lead from the front. They are usually back quite a way, out of range of any archers who might be feeling lucky, and they’re on a higher point so they can see what’s happening. If the general is in the middle of fighting, they’ll have no idea their left flank is crumbling and needs reinforcements, for example. 
And acid cannons seem like they’d be pretty volatile, the kind of thing you separate from the bulk of the army. 

I could have the general on a large tower overseeing the thing. He wouldn't have to worry about archers, however. But you are right in that I do need to leave some things open for player interpretation. As for the acid canons, well, the boss isn't too concerned with his troops wellbeing.

While he mentions his own warfare system in this video, Matt Colville talks about some things which are worth considering.