A great tactic to use both for the single player campaign, as well as for online multiplayer is to lean while you shoot. This allows you to stay partially hidden behind cover while also being also to shoot at your enemies at the same time. It's great for taking out enemies quickly, but it offers much less stability compared to crouching or standing up, so it has some downsides to it as well. However, you should definitely learn how to lean while shooting in Call of Duty: Modern Warfare, and you are in the right place.
In order to lean out from cover while shooting, you firstly need to hide behind a cover of some sort. This can be a door, a wall, waist high objects like boxes and things like that. When you are hidden behind them, press the L3 button to lean out from cover. This applies to both Xbox One and PS4. To stop leaning, just move away from the object again. It takes a bit of time getting used to, but after a few tries you will get the hang of doing it quickly and flawlessly.