This article is from the Recreational Figure Skating FAQ, by Karen Bryden with numerous contributions by others.
Skate dancing uses the same skills as other forms of skating, but has
its own emphasis and sequencing. You may also want to get the
instructor to show you the steps for the introductory dances to get a
better feel for what's involved. The introductory dances require only
forward skating - no turns. When you do get to the turns, they'll be
Mohawks and then forward 3's. You'll probably find them easier to
learn in the dance context than in a "figure" or random class context,
particularly the Mohawks.
The main skills that you need to begin "dance skating" are an
effective forward stroke, the ability to hold inside and outside edges
(meaning you can glide around turns on one foot) and a reasonably good
posture. If you haven't mastered these yet, a lot of your "dance" time
will be spent working on basics.