I am going to answer this referencing the way it is handled in the campaign "Das Jahr des Greifen" for DSA 4.1, which as far as I know was never released in english. So expect an answer that is designed to explicitly work with the TDE-System (I am not sure how well it would work in 5, but it should be totally fine) - The answer will contain spoilers for this campaign, explicitly for the "Schlacht auf den Silkwiesen"!
General tips and tricks
A battle is a really big thing, and no one will be able to keep tabs on everything that is happening at once. Depending on the heros roles, they won't, either. They will know what happens in their immediate surroundings, but not much more...
Also keep in mind to assign appropriate roles to the heroes. This can be tricky in TDE, because it means that (if we assume a fight in the "Mittelreich") for example nobles will be part of the cavalry (most likely) or the commanding staff, while peasants will be part of the skirmishers. And if you have a dwarf he might get pulled to man the catapults...
(Optional) Before the battle
Give the heroes a chance to prepare for the battle, and get to know other fighters on their side, their commanders (if they have any) and similar things. This will allow the following battles to be more dramatic and more realistic. People they got to know and like will get killed or do heroic deeds, and the heroes will do the same. In "Das Jahr des Greifen", the training and a parade are both important stuff that happen beforehand. Sending (some) of the heroes to scout or help the preparation in any other way will let your players feel like they made a difference. (Remember this point, it will become important later, too!)
Part 1: Skirmishers
In "Das Jahr des Greifen", the beginning of the battle is played out directly.
The battle begins with the skirmishers of the human side advancing towards the battle line of the orcs, who respond with arrows. The first people that the heroes (at least those that where assigned to the skirmishers) know and like already die.
Then the human command orders the skirmishers to fall back, but the commander of the heroes unit of skirmishers does not comply and even starts attacking those who do retreat, naming them traitors.
some orcs swarm out to engage the retreating skirmishers, and the cavalry has to come to the rescue, involving the heroes that are assigned to those regiments. No real melee combat is fought, especially not with the skirmishers.
the skirmishers retreat behind the lines of their army to rest and lick their wounds
There is no real reason to roll many dice in this fight, other than occasional parries or maybe checks to grab wounded combatants and retreat with them. The heroes never come into attack range anyway, they might fire some arrows at the orcs, but even then there is no need to roll. This is just to show the players in what kind of fight they are. It is not something where they can just run forward and kill the enemy (which, to be fair, is not that often the case in TDE anyway)
While the skirmishers (and thus most of the heroes) rest, the book details the other things that happen on the battlefield. The orcs advance, the human cavalry rides to face them and drives them back... I will not repeat all of it in detail, as the heroes will never know most of it anyway. They should only hear rumors/stories from the soldiers that return from battle to rest and maybe their commanding officers. I can not tell you how your exact battle will go, of course, but as the heroes will not make that much of a difference (yet), you can pre-plan most of it.
When the heroes go into combat again (don't give them too much of a pause here), you can just cut to some interesting or key scenes on the battlefield, same as it is done in movies (you reference Lord of the Rings, which has some prime examples of that, too) - During these scenes, remember to focus on both sides of the battle: Death and destruction (especially if it seems their side is losing) but also heroic scenes for the heroes.
Examples from the campaign:
At night, the heroes are sent on a scouting mission. They see some orcs that summon an army of undead to attack the human camp directly, and have to run through a giant horde of undead back to the camp to warn them in time, all the while trying not to touch the undead
An orc shaman, flanked by some war ogres keeps casting light spells that blind the humans while their mainly undead enemies are not affected. The heroes accompany some mages, trying to sneak behind the lines of undead and get close to the shaman. They then have to protect the mages from orcs and undead until the mages can cast a spell in Unitatio (combined spellcasting in TDE) to at least drive the shaman away.
Handling the scenes that are not played out
"Das Jahr des Greifen" actually defines some rules for these (important: keep in mind that these where intended for TDE 4.1, and for a whole battle. YOu should not assign a high modifier just because someone fought in the front lines one time, but only if he was there constantly, for the whole battle. If you are playing TDE 5 or want it to not be that punishing, adjust the damage numbers a bit, especially because the armor values seem to be a little bit lower.):
First, assign a modifier to each hero, depending on how many battles where played out - and thus actually fought with the basic rules of TDE - in the time they fought (this is done after the battle is over, but you can do it after each day or something too, if you want):
- Modifier of 0: All fights where played out and/or the heroes where not involved in any fights.
- Modifier of 1: Most fights where played out and/or the hero is a normal "line-combatant"
- Modifier of 2: Some fights where played out and/or the hero always fought directly on the front line
- Modifier of 3: Almost no fights where played out and/or almost no one comes back from the battle alive, the hero had to undertake dangerous solo actions
This is only an example though, you will have to assign this modifier with gm fiat. The campaign says that you could also take into account AT and PA values of heroes and so on.
Every hero then loses (2d6 - Armor) * Modifier * 10% of the HP he had at the beginning of the battle. If he loses 100%, he reaches camp barely alive (in 4.1 this is around 5 HP, where you lose the ability to take proper actions in combat) - If he loses more than 100%, he is near death and gets rescued with 1 HP. If you use this rule for NSCs too, they die if they lose more than 100%. If you are playing 4.1, you can assign wounds (which are a mechanic different from HP loss and if I recall correctly are remodeled as "Pain" in TDE 5) as you like.
A hero with an armor value ("Rüstungsschutz") of 4 gets assigned a modifier of 2. His player rolls 2d6, resulting in an 8 minus his armor value of 4 = 4. Then he multiplies this 4 with his modifier of 2 for a result of 8. Finally, this result is multiplied by 10 to have the percentage of hit points he loses (not from his maximum but from the HP value he started combat with): 80%. He started combat wounded with only 10 HP and thus has 2 HP remaining after the battle.
(8 - 4) * 2 * 10 = 80
If the army is well equipped, your heroes regain an additional 1d6 HP per 7 Talent points that the healer has (most healers would have around 7 or 14 if they are really good in TDE 4.1, for 5 you might need to adjust these numbers a bit) - You as the gm decide how talented the healer they get is (depending on social status and what they did during the battle, for example) This of course replaces medical care done by other heroes, as per the rules.
As far as I know, TDE 5 does no longer have the concept of "Bruchfaktor", which determines how easy a weapon will break. For 4.1, every weapon used in battle has its "Bruchfaktor" increased by 1. The rest will have to be handled without mechanics supporting it (repairing armor, getting new ammunition and so on)