This is your first and most essential mission.
Everyone who might have a role in issuing a public warning should know how to do it in their sleep. There have been way too many public warnings that have gone awry for a variety of reasons. Your jurisdiction should not be one of them.
See this article from Government Technology magazine, Next-Generation Emergency Alerts — What’s Working Where? which is a bit of a misnomer. It isn't "next-generation," it is now, it is what we have currently. Two systems they did not mention were the Emergency Alert System (EAS) and the National Weather System's Weather Radios. Both are additional tools in the toolbox and you can't rely on just one. This is one time you use a belt-and-suspenders approach to getting the job done.
The only way to be sure that you and your staff know how to use these warning systems is to practice, practice, practice. You have to have it down cold! "Repetition is the mother of remembering!"