Bear in mind, the events at Kent State didn't happen in a vacuum, but were at the end of several days of riots and confrontations. On the evening of May 1st after a combination of "bikers and vagrants" broke into several storefronts and a bank after bars closed early in response to large protests earlier in the day. Anonymous threats and revolutionary rhetoric were sent to local shopkeepers and city government prompting the National Guard to be called in.
The next day the ROTC building on the Kent State campus burned down as a result of arson, a crowd attacked the firefighters who tried to fight the blaze. The National Guardsmen present fought with some, many arrests were made but the Guardsmen weren't well equipped to handle a riot situation only having M1 rifles with standard bullets, 12 gauge shotguns, bayonets, and gas grenades.
The next day the Governor also made a number of provocative statements implying that he was declaring a State of Emergency and martial law, but this never occurred. Many people on the ground believed that he had done so, however. This muddied the issue as to who was actually in charge on the ground and led to conflicting orders.
On the morning of May 4 a protest that had been scheduled on May 1st was prohibited by the National Guard, although they had no authority to do so because the Governor hadn't actually declared a State of Emergency. A group of 100 Guardsmen were present at the burned out ROTC building when the protest began at the Victory Bell across the Commons.
The Guardsmen attempted to break up the protest, and fired tear gas. The protestors retreated over a hill and into the football practice field, but could no longer retreat because of a fence. The guardsmen initially pursued, but faced with a large (as many as 3,000 to about 70) and hostile crowd turning on them they began retreating up the hill. When they reached the top of the his some 28 guardsmen fired, most into the air or ground but some into the crowd. The guardsmen then fled, further bloodshed was largely averted thanks to University Faculty action.
Eight Guardsmen were eventually indicted by a Grand Jury for firing into the crowd. They entered self-defense pleas, after having been involved in regular violence for several days the court accepted the plea and the case was dismissed in 1974. In 1975 a civil case was brought against 28 defendants and the State of Ohio, which was settled out of court in 1979 for $675,000 (paid by the State) and the guardsmen signing a statement of regret (which didn't include an admission of wrongdoing).
Citation: THE MAY 4 SHOOTINGS AT KENT STATE UNIVERSITY: THE SEARCH FOR HISTORICAL ACCURACY by JERRY M. LEWIS and THOMAS R. HENSLEY
In one of the quirks of history, the shooting of two protesting students on May 14, 1970 at Jackson State (and the wounding of many others) is too nearly forgotten. This event - which did not get its own [song](http://en.wikipedia.org/wiki/Ohio_(Crosby,_Stills,Nash%26_Young_song) - nevertheless added to the tensions of the time.