There are several routes to getting credentials and experience as a coach.
Actually having a clue how to teach a skating skill is something else.
I recently stood in a Beta class and had to listen to the young coach tell the class that there are three pushes in a backwards cross over. (There are not. Imaginary Internet Points for telling me how many pushes in a cross over.)
Here are some ways to learn how to actually impart the skills.
Literally go onto the ice and figure out what a swizzle, and a stroke, and a cross over are. Most coaches have been doing the lower level skills since they were 4 or 5 or 6 years old. They don't know how to teach a swizzle or a one foot glide, because they can't remember not having that skill. So pretend you're just learning and break down those basic skills.
Work with an experienced coach
Many ways to do this-- either just shadow a coach (essentially apprentice yourself to them) and observe their teaching methods and tricks. Do this at the tot and learn to skate levels. These are no less difficult to teach than high level jumps, and you'll find kids who have had good coaching at these levels have a much easier time higher up the levels.
Another thing you can do is join the PSA and actually contract with a Master rated coach to be a formal apprentice. This gets the Master coach educational credits that they need, and gives you the right to receive actual instruction, and not just observation. Some Master coaches will do this for free (thanks, Nick!), some may charge you a lesson fee.
Hire a coach to teach you how to teach. I did this-- actually took private lessons where the coach taught me teaching techniques. This also reassured that coach that I was serious about learning proper technique; she remains a friend and advocate to this day.
If you've already been hired, think of yourself as a student teacher and ask for classes as the assistant with a coach whom you admire. Some rinks actually have formal student teacher or associate programs. I frankly don't understand why EVERY rink doesn't have a program like this, but then they never seem to consult me about this stuff.
Coaches' continuing education
ISI, USFS Basic Skills, and the PSA all run local, regional and national seminars, which you can find out about from the various websites (see the Resources page). You do not always have to be a member to attend (although you will pay a premium if you're not). Many are free to members. Coaches love to gripe about these, but I've never been to a continuing education event where I haven't learned something. Always be open to hearing new skills, tricks, and teaching techniques. If you didn't grow up skating in the district where you're teaching, this is also a great way to meet the coaches, and skating directors, in your area.
It's teaching, not skating
So many coaches do not understand this. When you're on that ice at the head of a class, you are not a skater. You are a teacher. Being a good skater and/or having a really good grounding in skating technique, do not make you a good teacher. There are class management and student psychology skills that are as important as the skating technique. Look for seminars, read books about classroom teaching, talk to teachers.
Don't be arrogant
You are not God's gift to skating, even if you're Tarasova. Listen, learn. Don't snub the new coach, or the adult skater who's gotten into coaching. They are all resources. Assume that your first five years of coaching are your apprenticeship, and allow yourself the time to become a great coach.