Give her some space to calm down and collect her thoughts. Approaching her too soon after the argument will only result in further conflict. Putting a little distance between you will enable you both to cool off, as well as give you the opportunity to think about your own part in the argument.
Make the first move. When you feel calmer, approach your wife and ask her if you can talk about the argument. If she is still angry, back off and give her some more time. She may well come to you herself given time. It is important one of you take that important first step to open the lines of communication. Giving each other the silent treatment will not resolve anything.
Talk to your wife calmly. Avoid rehashing parts of the argument or trying to push the blame onto her. Your aim is to negotiate towards a peaceful reconciliation, not become involved in a power struggle with her to prove who is in the wrong.
Address your part in the argument and apologize to your wife. This does not have to mean changing your opinion or admitting you were wrong if you believe you were not. The apology is for your part in the confrontation and a signal that you will try to approach any future conflict in a different way.
Listen to your wife when she is talking to you. It is important you take the time to listen to what your wife has to say. Letting her speak uninterrupted will show her you value her point of view, even if you do not necessarily agree with it. It is okay for a married couple to have differing opinions, as long as you both learn to respect each other’s views.
Work towards a compromise that makes you both happy. If you want completely different things, you both need to accept that there will have to be some give and take on both sides. Remember you are a team, which is much more important than getting your own way or winning an argument.