Shortwave Radio!
You know that weird dude that never leaves his house down the street with that gigantic antenna? That guy's more important than you think.
Ham radio operators, or amateur shortwave radio operators, are more than just hobbyists who stay up late at night chatting with other ham radio operators around the world. They're also part of an unofficial but better-organized-than-you-think network of emergency communications.
Amateur Radio operators set up and operate organized communication networks locally for governmental and emergency officials, as well as non-commercial communication for private citizens affected by the disaster. Amateur Radio operators are most likely to be active after disasters that damage regular lines of communications due to power outages and destruction of telephone, cellular and other infrastructure-dependent systems. ...
Amateur Radio operators have informal and formal groups to coordinate communication during emergencies. At the local level, hams may participate in local emergency organizations, or organize local "traffic nets" using VHF (very high frequencies) and UHF (ultra high frequencies). At the state level, hams are often involved with state emergency management operations. In addition, hams operate at the national level through the Radio Amateur Civil Emergency Service (RACES), which is coordinated through the Federal Emergency Management Agency, and through the Amateur Radio Emergency Service (ARES), which is coordinated through the American Radio Relay League and its field volunteers. Many hams are also involved in Skywarn, operating under the National Weather Service and provide emergency weather information to the NWS for analysis and dissemination to the public. (Source, see also)
In the Internet era, it's easy to forget these important volunteer heroes. If a zombie apocalypse were imminent anywhere on the planet, you can bet every ham operator on the planet would know about it within 24-48 hours — and probably a whole lot less.
But would they be alone? Heck no!
Usenet and BBS services
You're in the 90s, and that means you're deep in the world of Dungeons and Dragons, PC gaming, AOL... and both Usenet and BBS.
Usenet (/ˈjuːznɛt/) is a worldwide distributed discussion system available on computers. It was developed from the general-purpose Unix-to-Unix Copy (UUCP) dial-up network architecture. Tom Truscott and Jim Ellis conceived the idea in 1979, and it was established in 1980. Users read and post messages (called articles or posts, and collectively termed news) to one or more categories, known as newsgroups. Usenet resembles a bulletin board system (BBS) in many respects and is the precursor to Internet forums that became widely used. Discussions are threaded, as with web forums and BBSs, though posts are stored on the server sequentially
Email today is not just ubiquitous, it's beginning to actually die out as people live their lives on their phones through social media. But in the early-to-mid 1990s, email was still very much the province of colleges, businesses, and the military. It wasn't that uncommon that people communicated more through Usenet than they did email. Whatever social media may be today, it can give its thanks to Usenet for creating the basic threaded conversation context.
But Usenet was a UNIX-oriented system, so you generally found more technically-oriented folks there. Where did the average high school teenager go? Dial-up Bulletin Board Systems (BBSs).
BBSes once numbered in the tens of thousands in North America. These mostly text-based, hobbyist-run services played a huge part in the online landscape of the 1980s and ‘90s. Anyone with a modem and a home computer could dial-in, often for free, and interact with other callers in their area code. (Source)
Organizations like America Online (AOL) were very much commercialized BBSs. But before they became popular, there were gazillions of grassroots BBSs that shared everything! But it was a somewhat short-lived fad (unlike Usenet, which is still going strong today).
Then the internet came along in the mid-1990s. Like a comet to the dinosaurs, it upended the natural order of things and wiped BBSes out. My system was one of the casualties, a victim of the desire to devote all my online time to the internet. The same scenario repeated itself on thousands of computers across the country until, one by one, the brightest lights of the BBS world blinked out of existence. (Ibid.)
There are still a handful of operating BBSs today, but it's a dying culture. But, believe me, those were the days!
And news of a possible zombie apocalypse can probably be found on any of these services right now.
But there's one more: the EBS
There's something you very, very, very rarely hear about today, the Emergency Broadcast System (EBS). I grew up regularly seeing and hearing tests like the one I just linked to.
The Emergency Broadcast System (EBS), sometimes called the Emergency Broadcasting System or the Emergency Action Notification System (EANS), was an emergency warning system used in the United States. It replaced the previous CONELRAD system and was used from 1963 to 1997, at which point it was replaced by the Emergency Alert System. (Source)
The EBS has been replaced by the Emergency Alert System (EAS) which can (and does) operate through cellphones. The EBS was used more then 20,000 times (though never for anything big like a nuclear... or zombie... attack). The EBS would be the official way of hearing the announcement.