So you're in the back of the classroom helping a student and suddenly you hear a commotion from the front of the room. All your students are out of their seats shouting "Fight, Fight, Fight!" and two kids are pushing eachother. What do you do? You missed how it all started. Of course you immediately break up the fight and tell the kids to go back to their seats (if they don't they can join the fighters in the Principal's Office). You and the two kids step aside to talk about it. There are two sides of every story, and that's quite obvious now.
This is what I would do...if anyone is hurt, send them with another student to the nurse. If no one is hurt, write them up, and call the office to send someone down to pick them up. Often, when things calm down and get more serious in the office the truth comes out. As far as the other kids who were shouting, they just saw you in action and know you're serious about behavior.
For less serious offenses that you did not witness such as swearing and misuse of art supplies, rather than trying to find out the culprit, remind the entire class that this is unacceptable and that you will be watching more closely from now, unless you get a confession.