Well first of all from Tolkien's sources we know that the Uruks of Mordor are simply a "race of black Orcs of great strength" that appeared several hundred years before LotR, at the time of the reign of Ruling Steward Denethor I in Gondor (Denethor II is the one that appears in LotR narrative). The Orcs as a race of course are abusive a bit and conflicted among themselves, they kill each other but mostly between different tribes or groups. There are feuds among them, there is strife and treacheries, the Orcs themselves are also varied in their personalities, manner of speech and behaviours, strengths and skills. There is rivalry but also uneasy "friendships", alliances (often with Wargs who are intelligent creatures, though of bestial shape and manners) or sense of camaraderie (but sentiments are not too deep). There is also surprising loyalty between Orc chieftains and their bodyguards (who appear to be similarly tough like the chieftains themselves), but the examples of such things come from more or less independent societies of Orcs in the Misty Mountains:
Thereupon Azog came forth, and he was a great Orc with a huge iron-clad head, and yet agile and strong. With him came many like him, the fighters of his guard, and as they engaged Náin's company he turned to Náin, and said: "What? Yet another beggar at my doors? Must I brand you too?"
The Lord of the Rings, Appendix A, III "Durin's Folk"
[...] and with them came the bodyguard of Bolg*, goblins of huge size with scimitars of steel.
The Hobbit, Chapter 17, "The Clouds Burst"
*Bolg is the son of Azog and approximately about 140 years or more old at the time of Battle of Five Armies a strong leader that united Orc tribes from Misty Mountains (that already were enraged, some wanting to avenge death of the Great Goblin, they also wanted to take Smaug's treasure and "resolved now to win the dominion of the North.")
"Though Orcs will often pursue foes for many leagues into the plain, if they have a fallen captain to avenge."
The Lord of the Rings, Book II, Chapter 6 "Lothlórien"
'Not our orders!' said one of the earlier voices. 'We have come all the way from the Mines to kill, and avenge our folk. I wish to kill, and then go back north.'
The Two Towers, Book III, Chapter 3 "The Uruk-Hai"
Azog viewed himself as independent king in Moria:
"If beggars will not wait at the door, but sneak in to try thieving, that is what we do to them. If any of your people poke their foul beards in here again, they will fare the same. Go and tell them so! But if his family wish to know who is now king here, the name is written on his face. I wrote it! I killed him! I am the master!"
The Lord of the Rings, Appendix A, III "Durin's Folk"
Though as Gandalf said, Orcs many times plundered Moria; and the mithril that was brought up to the surface by dwarves, was paid by the orcs as a tribute to Sauron, those Orc clans and tribes of Misty Mountains and Grey Mountains appear to be accustomed to independence, and they set up the petty realms of their own with their capital at Mount Gundabad and local strong leader like the Great Goblin of Goblin-town at High Pass (and he had also strong personal guard numbering some 30 or 40 armed guards). Sauron also felt it necessary to populate mountains with his own servants so they would establish obedience towards him easier by meddling in local Orc-policies. (To save him bother, but Sauron also has abilities to dominate minds of his servants and can lure the wicked things, draw to Mordor or any other place he resides, bending his will for that purpose, he also can control his armies with peculiar example of mind control, drive them directly by his will, filling them with hate and fury.)
As mentioned earlier they can cooperate, held council together either because being united against a common enemy, or by skills of a strong orc-leader (or by superior will of Dark Lords).
In armies of Mordor there appears to be some sort of hierarchy, each Orc it seems has its name, number, military rank:
'You come back,' shouted the soldier, 'or I'll report you!'
'Who to? Not your precious Shagrat. he won't be captain any more.'
'I'll give your name and number to the Nazgûl,' said the soldier lowering his voice to a hiss. 'One of them's in charge at the Tower now.'
The Return of the King, Book VI, Chapter 2 "The Land of Shadow"
There are of course examples of Lieutenant rank in Mordor, like Lieutenant of Barad-dûr, a Black Númenórean known as Mouth of Sauron, sorcerer, herald and ambassador of Mordor; a man "more cruel than any Orc" but still a mortal man of enhanced race and abilities. Another is Lieutenant of Minas Morgul known as Gothmog (not to confuse with the ancient Lord of Balrogs, servant of Morgoth who often fulfilled the role of field general), but his kind is not revealed. We don't know what race he was; certainly he was second-in-command of the Witch-king who ruled the fortress (there was also force of cavalry in there, riders on horses robed in black, most likely Men possibly so corrupted that the power in Morgul Vale did not affect them as much "because of the evil that dwelt in that valley, where the minds of living men would turn to madness and horror"). Also Orcs stationing in those strongholds were well equipped, those of Barad-dûr were 'heavy-armed' ("A troop of heavy-armed uruks from Barad-dûr...") and those of Minas Morgul had fine and well-fit gear bearing emblem of the fortress.
The Orcs can give aid to each other in certain circumstances, even keep their word but also slip into in-fightings. There are Orcs who were bred to service, those recruited from pre-existing population, and they have varying degrees of loyalty and sense of duty. Some as seen in one quote are dutiful soldiers who would discipline others at the sign of 'rebel-talk' others have their own motivations and purposes. There are those who fulfil orders and those who serve unwillingly:
They were a gang of the smaller breeds being driven unwilling to their Dark Lord's wars; all they cared for was to get the march over and escape the whip. Beside them, running up and down the line, went two of the large fierce uruks, cracking lashes and shouting.
ibid
Sauron can of course enforce order and efficiency in all operations, as he is micro-managing his realm, and his mental powers allow him to dominate minds of Orcs often to such extent that they can become almost mindless for a time after his will is removed. Of course as mentioned there is still in-fighting in Mordor either because keeping all of them in total mind control is a straining task and he does not control them that way all the time or it's a by-product of him filling them with "hate and fury" so to make them fight better. :) When such control is removed the Orcs might neglect their orders or engage in as independent beings, but it is always easy for Sauron to dominate his creatures and servants. For Sauron Orcs are useful slaves and he has them in plenty.
The Orcs in independent communities act more like gangs of robbers, raiding Vale of Anduin for slaves and spoils. As we see them in 'natural environment' so to speak:
It was lit by a great red fire in the middle, and by torches along the walls, and it was full of goblins. They all laughed and stamped and clapped their hands, when the dwarves (with poor little Bilbo at the back and nearest to the whips) came running in, while the goblin-drivers whooped and cracked their whips behind. The ponies were already there huddled in a corner; and there were all the baggages and packages lying broken open, and being rummaged by goblins, and smelt by goblins, and fingered by goblins, and quarreled over by goblins.
The Hobbit, Chapter 4 "Over Hill and Under Hill"
The Orcs can also share things, help each other out in some measure:
'I gave him better than I got, but he knifed me, the dung, before I throttled him.
The Return of the King, Book VI, Chapter 1 "The Tower of Cirith Ungol"
"D'you remember old Ufthak? We lost him for days. Then we found him in a corner; hanging up he was, but he was wide awake and glaring. How we laughed! She'd forgotten him, maybe, but we didn't touch him—no good interfering with Her."
The Two Towers, Book IV, Chapter 10 "The Choices of Master Samwise"
"Mauhúr and his lads are in the forest, and they should turn up any
time now".
The Two Towers, Book III, Chapter 3 "The Uruk-Hai"
(when Ugluk was waiting for reinforcements, they arrived to help in fight with Rohirrim but did not succeed)
As you see there is a bit of hypocritical humor, the Orcs apparently also have certain notions of things which are acceptable and which are not (they are also convinced that their enemies like Elves are worse than they are):
"He may have had nothing to do with the real mischief. The big fellow with the sharp sword doesn't seem to have thought him worth much anyhow — just left him lying: regular elvish trick."
The Two Towers, Book IV, Chapter 10 "The Choices of Master Samwise"
The Orcs themselves are also skilled craftsmen and labour force. Some Orcs were also skilled commanders. Mordor was also rather well organized, well maintained infrastructure, roads and bridges in constant repair, good fortifications and garrisons in strongholds, patrols (not only Orcs but horse riders), clear chain of command and some mysterious way for exchanging messages. Of course Sauron has telepathic abilities but there is some way news is exchanged quickly between Lugburz/Barad-dûr (the Dark Tower) and other fortresses:
"Down in the dark trough, cut off from the dying glare of Orodruin, Frodo and Sam could not see ahead, but already they heard the tramp of iron-shod feet, and upon the road there rang the swift clatter of hoofs.
[...]
He let go. Frodo followed. And even as they fell they heard the rush of horsemen sweeping over the bridge and the rattle of orc-feet running up behind.
The Return of the King, Book VI, Chapter 2 "The Land of Shadow"
Beyond its stony course they saw a beaten path that wound its way under the feet of the westward cliffs. Had they known, they could have reached it quicker, for it was a track that left the main Morgul-road at the western bridge-end and went down by a long stair cut in the rock to the valley's bottom. It was used by patrols or by messengers going swiftly to lesser posts and strongholds north-away, between Cirith Ungol and the narrows of Isenmouthe, the iron jaws of Carach Angren.
ibid
"As far as their eyes could reach, along the skirts of the Morgai and away southward, there were camps, some of tents, some ordered like small towns. One of the largest of these was right below them. Barely a mile out into the plain it clustered like some huge nest of insects, with straight dreary streets of huts and long low drab buildings. About it the ground was busy with folk going to and fro; a wide road ran from it south-east to join the Morgul-way, and along it many lines of small black shapes were hurrying.
'I don't like the look of things at all,' said Sam. 'Pretty hopeless, I call it — saving that where there's such a lot of folk there must be wells or water, not to mention food. And these are Men not Orcs, or my eyes are all wrong.'
Neither he nor Frodo knew anything of the great slave-worked fields away south in this wide realm, beyond the fumes of the Mountain by the dark sad waters of Lake Núrnen; nor of the great roads that ran away east and south to tributary lands, from which the soldiers of the Tower brought long waggon-trains of goods and booty and fresh slaves. Here in the northward regions were the mines and forges, and the musterings of long-planned war; and here the Dark Power, moving its armies like pieces on the board, was gathering them together.
ibid
As a fun-fact I might add that the one minor difference in comparison with game is that Orcs in book wore more clothes and had more common equipment :)
He opened the bundle. Frodo looked in disgust at the contents, but there was nothing for it: he had to put the things on, or go naked. There were long hairy breeches of some unclean beast-fell, and a tunic of dirty leather. He drew them on. Over the tunic went a coat of stout ring-mail, short for a full-sized orc, too long for Frodo and heavy. About it he clasped a belt, at which there hung a short sheath holding a broad-bladed stabbing-sword. Sam had brought several orc-helmets. One of them fitted Frodo well enough, a black cap with iron rim, and iron hoops covered with leather upon which the evil Eye was painted in red above the beaklike nose-guard.
'The Morgul-stuff, Gorbag's gear, was a better fit and better made,' said Sam; 'but it wouldn't do, I guess, to go carrying his tokens into Mordor, not after this business here.'
The Return of the King, Book VI, Chapter 1 "The Tower of Cirith Ungol"
