Join a club or association and train with a licensed square dance teacher. See Resources for recognized organizations.
Rehearse saying square dance figures on a microphone in your basement or any other secluded place. Make sure you do not practice anywhere where people might get annoyed or hear you.
Consult other square dance callers. Ask them about what steps they took to get their gigs. You might find that many actually square danced before taking on the role of caller.
Ask another caller if you can be a co-caller or shadow on a square dancing night. See how you feel about speaking on the microphone and directing a bunch of people. This position will help you know if you are suited for this job or not.