Composure
If you find yourself in a conflict, the first step to de-escalation is to regain your composure. Once you are calm, you will automatically start to de-escalate the situation, as it takes more than one person to both start and maintain a fight.
One of the more difficult tasks in learning to maintain or regain your composure is recognizing when you have become emotionally triggered, and are therefore no longer thinking clearly.
When we are triggered - most likely caused by something someone says - our bodies experience a surge of adrenaline, which causes us to sweat, our heart to race, and for us to breathe more quickly. A surge of adrenaline also has the effect of decreasing the activity in our prefrontal cortex, which is the part of the brain responsible for self-control, planning, and problem solving. Poker players call this phenomenon being, "On tilt," and is used to describe situations where a player has become so emotionally triggered that they are playing irrationally.
This then poses a problem, as when we get triggered by something someone says, we stop thinking clearly, which in turn reduces our awareness that we have become triggered. As we lash out at whatever triggered us, other people may be triggered by us, causing them to lash out, which in turn causes us to become more triggered. This is how conflicts can escalate out of control, and become all-out fights where people have stopped thinking logically, and are only concerned with winning by any means necessary with no regard for long-term consequences.
To detect when we have become triggered, we must become aware of our neutral emotional state, which is to say, our emotional baseline. The process is often referred to as mindfulness, and is usually associated with meditation, but can also be thought of as simply being aware of how you feel normally when you are not feeling any stress: such as how fast you usually breathe, how clearly you usually think, or even how fast your heart typically beats. When we deviate from these norms, that is a good indication that you have become triggered.
Let's say you were in a meeting, and you have just given a demo of your work to your team. Being mindful of your emotional state, you note that you are calm, thinking clearly, breathing normally, with your heartbeat hardly noticeable. A colleague then says, "I hope you didn't spend a lot of time working on this. It's trash and we would never use it. You might as well delete it and start over, and should probably rethink if you're serious about this line of work." At this point, you notice that you're starting to sweat, your heart is pounding in your ears, you're breathing rapidly, and you realize you are what is often called, "Seeing red," as you can no longer think clearly. If you are like most people, you will have a freeze, flight, or fight reaction, in that you may freeze in place, being so shocked you don't know what to say, you may try to run away by wrapping up the meeting as quickly as possible, or you may want to fight. As in a professional workplace freezing in stunned silence, or running away is not acceptable behavior, many people instinctively fight without even noticing that they were triggered.
Unless you can return to your baseline emotional state, where you are calm and thinking clearly, your primal instinct will most likely take over, and you will say, "I don't know who you think you're talking to, but I don't need you to judge my work. You should take a long look at the garbage you're putting out before you start pointing the finger at me!"
Saying this would be what is called a "career-limiting mistake," in that simply by allowing yourself to react while in a triggered state, you have said something that can permanently damage your reputation and therefore your career progression at your company.
Provided you were mindful enough to recognize that you were triggered, however, your first step should be to calm yourself down, which primarily involves breathing deeply. To do this, simply inhale a deep breath in through your nose, and exhale slowly out through your mouth. After doing this a few times, you should begin to regain your composure.
Breathing deeply also has the effect of you not responding immediately to your colleague's attack, which both creates an opportunity for other people to intervene on your behalf, as well as gives you a chance to think of a response. Often, simply slowing down the pace of a conflict serves to de-escalate the situation, as it gives people a chance to think about what just happened, and how they should react. Sometimes, just the awkwardness created by the silence of you not saying something will yield an apology from an offending colleague, as they realize the impact of what they said.
Stopping and controlling your breathing also has another incredibly interesting side effect, in that people may begin to mirror your body language. Mirroring is when people unconsciously mimic the body language of someone they are observing, such that when we see someone breathing deeply, we may soon find ourselves breathing deeply as well. The effect of mirroring can be further leveraged by you speaking slowly and softly. All of these actions together can have the effect of people mimicking your behavior unconsciously, which in turn can have the effect of them becoming calmer.
Returning to your colleague, after the awkward silence created by the time taken for you to take a few slow, deep breaths, you might then choose to say slowly and softly, "I didn't realize you felt that way," at which point you might slowly sit down. To maximize the de-escalating effect of your body language, you might also keep your hands in plain sight, perhaps with palms facing towards the person, while lowering your eyes so as to break eye contact.
If done correctly, you should now be composed, the room should be calm, and your colleague should feel very foolish, and be quite embarrassed. By quickly regaining your composure and de-escalating the situation, people will regard you as being a mature professional, and regard them as being rude, disrespectful, immature, and unprofessional. How the situation is handled going forward is its own matter, but at least a conflict is avoided, and the situation de-escalated before it spiraled out of control.