Ballroom dancing is a general term which includes many dance styles, depending on your perspective.
Most ballroom dance styles originated from social or folk dance styles of the past. In many cases, the casual variations of these ballroom dances are still danced as folk dances or at social dances around town, and often close to their original forms.
But modern ballroom dancing, competitive dancing, or dancesport, is formalized and has embellishments that are often very different from the original dance of the same name, though the basic steps may be similiar.
Whether you intend to progress to ballroom competition, or just learn some casual dance steps for fun, or as a wedding dance, you can learn from classes offered by school board adult education classes, or through several great professional dance schools in the area. They also often offer 'practice' nights which are more casual dance events for learning and socializing.
Rules and competition in dancesport is formalized by two major organizations, with sightly different instruction methods.
And there is a form of ballroom called 'Round Dance' that is choreographed by a caller.