Keep your emotions in check. Do not get angry or heated. Understand that arguing or fighting will NEVER end in a positive conclusion. The only way an argument can have a positive outcome is if one person is fully convinced by the other person that they were wrong the other person is right, and that happens in 0.000001% of all arguments.
Arguments often start because a woman is unhappy and experiencing emotion as a result of it and she is not always able, or willing to directly tell you what the problem is. Unfortunately it is the man's job to decode the real underlying reason for her anger. Yes that is an unfair burden for men but so is life and we have some things much better than women so you will have to learn to take this in stride.
My formula for an "argument" is simple, and it works well:
1. Do your best to keep anger in check, and try to envision yourself on the same side of the fence as her, looking to solve a problem together.
2. Listen to what she is saying or complaining about etc. Like really listen. Ask questions. Repeat some of the things she says to demonstrate you are listening, hear and understand her. Then explain how you feel about it. You don't have to agree with her, nor she you. The point is to explain to each other how you each are feeling. That won't be enough for her, usually, and she will generally want you to admit to be being wrong (even if you weren't) but do NOT do that (unless you do feel you were wrong). At this point she will likely want to engage you in circular arguing which you must put an immediate stop to by ending the discussion entirely. Once she has said her piece and you have said yours, you say, "I have heard what you've had to say. I understand you. I hear you. I have told you how I feel about it and it doesn't seem we are going to agree on this. More discussion is not going to change either of our minds and arguing won't help us so we are going to have to drop this and move on now." Then refuse to engage her certain attempts to continue arguing with you.
3. Don't take women so seriously. They say a lot of sh*t they don't mean and they feel in-the-moment. You just have to accept that. However, if they get downright nasty, insulting, or out of line, draw a boundary CALMLY by describing what they said/did that was inappropriate and tell them it is not acceptable tfor her to talk to you that way and if she pushes back on that then you end the conversation and tell her you'll talk later when she has calmed down. Leave if you need to or ask her to leave.
In either of the last two situations where you are ending the conversation, get ready for her to get even madder and accuse you of controlling the conversation, being a hypocrite, "shutting down", whatever. This is where you need to understand, accept, and believe in masculinity vs femininity. Contrary to what a woman tells you, it is NOT WRONG to end a conversation just because SHE doesn't want it to end. In reality, you are doing her a favor because she is overwhelmed by her emotions and can't control herself. As a man, you can. You must ignore her accusations/insults about your shutting down the conversation, and take space until she calms down. She will complain about your taking space too but that should be ignored as well. Leave the house if you have to or ask her to leave.
Sometimes it helps to think of women as children having their temper tantrums. Women are ruled by their emotions, just like children, so it helps you not take them so seriously when they are in this state.
It can also help to sit down next to her, try to re-frame the situation/mood, hold her, tell her "hey, what's this all about? You know we are good? This isn't that big of a deal is it? I love you." This can be very difficult because the last thing most of us want to do when a woman is acting-out and criticizing us and treating us unfairly is to go to her and hold her, but often times this is what is needed most, and of equal importance, if you HAVE made this offering to her and she still refuses it, then you can be even more comfortable, certain, and confident that you have done everything you can in this situation and the conversation must end here and now and no matter what she says to push back on that, you are making the right move to shut it down.
Do not argue with women. And do not let a woman convince you that you are wrong for shutting an argument down AFTER you have heard what she has to say and truly listened to her. These two points are critically important.