It takes two to argue. If you don't answer back, there cannot be an argument. Just say, "I don't want to talk about it now" and just softly repeat that phrase.
Arguments escalate with the volume of the arguers."A soft answer turns away wrath" (Proverbs 15:1). The more forceful the other person argues, the quieter your response becomes. You will see the other side tone down his/her voice in response.
You can't have an argument if you agree. "That's a good point." "I hadn't thought about that." "You are definitely right." Focus on where you can agree, not where you differ.
Admit you were wrong. No one is ever totally right. Find something to apologize for, to take responsibility for. The other person will feel better and may even own up to some mistakes of his/her own.
Do not accuse or attack. Don't say, "You said this!" "You did that!" Ask questions, don't make statements. And ask questions with sincerity not as a cutting sword to make an attack.
Remember your goal! In the case of marriage, you want harmony, peace, a good atmosphere, love. Arguments breed stress and anxiety, not peace and pleasantness. Tell yourself: I love my spouse, I love my kids, I love my money (divorces cost a lot of money).
Don't show disrespect to another person by saying things that are damaging, mean or not worthwhile. This especially applies to one's spouse. Remember, you chose your spouse over every other person on this planet!
Turn the argument into a discussion. Don't defend a position; set forth an idea or problem to be clarified. People of good will who reason together can come to a common conclusion. Listen with an open mind. Be a judge, not a lawyer! Although Lawyers are very important at the right time. Love your lawyer!!
Ask yourself, "Is this argument really worth it?" In the end, whatever you are arguing about may be ultimately trivial. Likely, there are other issues regarding communication, respect, responsibilities which create the angst and anger leading to arguments -- rather than discussions.