"Dance like it's the last night of the world."
"Rags To Riches" by Tony Bennett
The movements of each dance are broken down, for teaching, into named figures, each consisting of a few actual steps. For example a figure called the "Reverse Turn" exists in different forms in many dances, and usually has 6 steps. Roughly 200 figures exist for each of the Ballroom and Latin dances, and each figure takes about an hour of instruction and practice to master. For social dancing, learning a dozen or so basic figures in each dance is sufficient,
"I Can't Get Started" by Bunny Berigan
Most syllabi were made up by profession teachers using the steps that they were more acquainted with, instead of teaching movements. The most basic of course is the walking step, left, right, left, right etc. It is used in two count, three count and four count measures. The lead may go forward, backward and to the right or left sides. A very obvious variation is the "promenade" in which the partners can get side by side and walk forward together. Street dancers are the ones that learn to use these movements very well in dancing to any kind of music.
"At Last" by Glenn Miller with Ray Eberly on vocals.
The most famous walking step is the American Waltz. Just left, right, left, 1, 2, 3. Then right, left, right, for another 1,2,3. But it should be obvious that dancers can do all of these wonderful things in hundreds of different movements. And most are just walking steps. The Viennese Waltz is somewhat different, naturally. The Latin version is danced with a chassé basic.