As opposed to a local tragedy that slowly got picked up by bigger news stations over time.
I perceived, for example, that the Sandy Hook shooting was national news the same day, within a couple hours of the events. Were the events of the Columbine shooting broadcast nationwide immediately? How would the average person have heard about what had happened?
Yes. It received extensive media coverage (both on TV and in print) at both the national and nationwide local level both immediately and for days and weeks afterward as more details came out. Meaning that if you were basically anywhere in the US you would see coverage of Columbine on the national TV news, your local TV news stations, "national" newspapers (nytimes, usa today, washington post, etc.), and your local newspaper (which still existed at the time). This included unscheduled "special reports" by national news that interrupted regular programming on the day of the event while it was still active (or perceived to be). There were also presidential news conferences and statements on the massacre as well.
Some collections of coverage: