Darkness is your friend

The game does a mediocre job of describing this, but yes, darkness is your friend in this game. In the dark, AI vision cones are drastically reduced; they will not see you unless you are very close to them. While you are in the darkness, your game turns black and white (can be removed via mods). You'll generally want to stay in the shadows as much as possible. Additionally, NPCs will not see bodies as easily in darkness as they would in light, so take this into consideration next time you see a group of enemies in a dark area. Despite all this, their hearing is not impacted when you are in darkness, so do keep that in mind when CQC'ing a helpless thug.

Furthermore, you should be trying to make your own path whenever possible. There are tons of lights you can shoot out in order to make traversing an area much easier (will go into more detail on this in the next section). Shooting lights is arguably the best way, because it permenantly disables the source, unlike EMPs which are only temporary. Though EMPs can be a good way of quickly flanking if you are close to enemies. They also stun the enemies themselves, so use this as an opportunity to get a few free kills.

Know your enemy.

Going into a deniable ops unprepared can lead to a lot of undesired consequences. So, this section will help to prepare you.

AI have, what I like to split into, 3 "modes".

Passive Mode
In this mode, NPCs will go about their preset paths, whether that be standing guard, patrolling around, or chatting up another guard about how many times you restarted the level to get those PEC challenges. In this mode, NPCs are essentially at their weakest. The easiest mode to deal with, and the most desirable. Following this guide can help you to keep them in this mode.

Suspicion Mode
Let's say an enemy heard an explosion, or you made a loud noise, or someone discovers a body. The NPCs will not be happy, and will begin breaking off from their preset paths and will start patrolling around to find you. This is often accompanied by flashlights, which give NPCs a much greater vision cone in darkness. They will remain in this mode (typically) until they die. So when you do get them in this mode, good luck keeping it that way. The best counter to this mode is to simply be stealthy and pick enemies off. Keep in mind any more bodies / explosions / loud noises wont impact them any more in this mode, so feel free to be as reckless but as stealthy as you wish.

Assault Mode
When you are spotted / make too much ruckus, you will alert the enemies, and they will begin moving towards your LKP (last known position). In this state, they will often shoot you as soon as they see you, without doing their usual shocked animation when they detect you. This mode gives you the opportunity to flank around, and if you keep making noise deliberately, you can abuse your LKP to lure enemies to open areas. Although, sometimes enemies won't chase you down, and will permenantly wait for you to come to them. In this case, you'll just have to kill them.

A few extra things to note. You can often just run up to people and melee them in any "mode", though enemies in suspicion or assault mode will push you away if you try to melee them.
And laser sights make the first two shots of assault rifles 100% accurate, so you can quickly kill helmeted enemies with them.
And also, you can shoot out at least 2 lights nearby an enemy before they get suspicious and try to pinpoint your location. If enough enemies notice the ruckus, you will gain a LKP and enemies will enter assault mode. Although if you take out the enemy who caught you out, you could get away with it.
You can't break stealth as long as you have not been detected. To my knowledge, getting a LKP won't count as breaking stealth, but do correct me if I'm wrong.