I try to be proactive when on duty and being a big bugger with a loud voice, duty is usually pretty easy for me. Even still, I am often called upon to break up fights that happen on my watch.
I use a simple strategy - DISTRACT + DIFFUSE + DISPERSE that (usually) works.
Firstly, DISTRACT students from hurting or hitting - what ever is occurring. This might might be a whistle or calling out. (Water on the fighting dogs!). The aim is to get the offenders to focus on you, not each other. ("I'm here gentlemen/ladies. Look at me!" - repeat this calmly.). If you can use humour, now is a good time to apply it. If not - DON'T.
Never get in the middle, no matter how big you are. I've been dropped by a wayward kick from a preschooler.
Secondly, DIFFUSE the anger by NOT being angry yourself. (Riots develop when both sides are angry.) Avoid shouting or panicking. Be calm - at least sound calm. Keep your directions short and clear. Never give more than ONE direction at a time.
"Bill, thanks for standing over there. John, thanks for putting your hands down." Repeat if necessary but do not change the directions. "OK. Let's sit down and face opposite directions." Having students sit on the ground really has a calming effect. (Watch what NYPD do) and then handcuff them to the nearest pole (joking).Thirdly, DISPERSE. You only need the offenders. Chase the watchers away. (Move on citizens. Nothing to see here)
The next step depends on your level of authority. If you are comfortable dealing with the offenders at this point, then do it. I suggest, if you are a relief teacher you probably need to pass the offenders over to some one. Now ... that is another article!