Do you mean a person who makes their living from ballroom dancing or a person that competes as a professional.
In either case the most common route is taking lessons at a studio or taking a job at some studios that will teach you. A lot of people that want to compete, work for studios that provide traing and coaching for competition for their employees.
Lots of people start with the big chains, to get training and develope theiur teaching skills. Than move on to being an independant teacher.