I could tell you about mastering the art of teaching dance, planning lessons, making sure your students have clear learning outcomes, and continually improving, but I'm also assuming you know you need to do that, too.
Instead, I'll say that dance organizers tend to be a pretty risk averse crowd, generally speaking. Organizers hire instructors who they think will draw students, whose dance values align with their own, and who will be responsive, on time, flexible when shit hits the fan and generally pleasant to work with.
Folks who win competitions at big weekends often have members of the audience wanting to take classes from them.
Folks who do really awesome choreographies at big weekends also tend to have audiences who want to take classes from them.
It can also help to have a specialty that has a catchy name that the national scene is clamoring to learn.
The professional and pleasant tend to come through networking, personal interactions, and through word of mouth from students and other organizers. This is partly of why many instructors include quotes from students and organizers on their websites.
If you think you're doing all of this and you're still not getting hired, be patient. It can take years to get the recognition needed to make an organizer feel secure in hiring you. And never stop learning!
by Paul Mandel