This article is from the Recreational Figure Skating FAQ, by Karen Bryden with numerous contributions by others.
Cross-overs are much like walking sideways up a set of stairs. They
are done on a circle and since you are moving, you will be leaning
into the circle and will be stepping "up" into the circle. For both
forward and backward crossovers, the skate on the outside of the
circle crosses in front of your other skate.
If you are doing it correctly, like climbing stairs, you are
sequentially transferring your weight to the inward (upward) skate,
and then balancing on it as you swing the other foot into position for
the next step. If your weight is not balanced on your skating leg then
yes, you will lose your balance (but this isn't how it's supposed to
Try thinking of it this way: All of your body's weight should be
balanced over the tracing. What you are doing in crossovers is
changing which foot is carrying your weight. You place the "new" foot
under the center of gravity, and push the other foot out of the way.
Suggestions for cross-overs are:
1) DO lean into the circle
2) shoulders are NOT square to the trace or arc, they are turned
INWARD towards the center of the circle and the arms should extend
along the line of the shoulders.
3) knees should be well bent the entire time
4) don't raise up between strokes, stay down
5) for freestyle, a good crossover is deep with legs crossing above
the knees; for dance, crossovers should be more shallow.
6) strokes on both feet are power strokes, done with a clean edge
leaving the ice. (On forward cross-overs it may be helpful to think of
pushing with the heel of the inside foot in order to alleviate the
common problem of scraping your toe pick.)
7) definitely all strokes are with edges.