It's never easy stopping an argument once it's in full swing, so I guess the best way is to avoid it before it gets too heated. I've always heard the best way to stop a fight if you SEE one that you're NOT involved with, is to scream out "Hey Here come the Cops!" and that usually jolts the people back into a reality check and they break it up. But if you yourself are getting into a heated argument, consider these things:

What’s the Best Way to Stop a Fight?

Take turns saying what you really like about the other person.

Quit talking until the other person calms down.

Say that the conversation is getting heated, admit you had a part in that, suggest a break, then leave instantly but work to resolve the problem when you get back – don’t just leave.