Ladies,
As a recent masterer of basic sidehilling and a husband of 20+ years (I schprecken der wimminish) may I add a couple things?
If your area has any long, even slopes where you can line yourself up in the direction of the valley, try practicing there first. This allows you to ease into the hill and pull a long sidehill without having to climb too high on the slope. IF you do wipe out practicing you're not yardsaling your sled down the mountain. U-shaped glacial valleys are perfect for this (assuming the avy danger is low)
You can practice in both directions until you build some confidence then you can move onto turning out of short climbing runs into sidehills. From there you move to turning back uphill and reversing directions.
By the way, the physics behind why countersteering works is about balance and inertia. A sled is inherantly unstable in a turn because it only has 3 points of contact--the track and ski's. We all know instinctively to lean into turns so we don't flip over the high side. This is great advice. I was never told that.
In a sidehill we are using that instability to counteract gravity. By turning the skis out and leaning we are forceing the sled to tip into the hill. When we do it just right our lean equals the downhill pull of gravity and we crab across the hill in a straight line. Taminator's pics two posts up are a perfect example of this in action. So, where does the "dirty leg out" come in doing this? That is what I have been told to call it. I am somewhat uncomfortable putting my left foot foreward, with my hanging out right leg on the right side of my sled. How do I over come this? And, how do I switch back to the correct foot on the correct side?
Practicing figure 8s in the meadows is great practice and doesn't hurt if you make a mistake.
Also, generally speaking, if you are right handed you will have an easier time mastering sidehilling on your left side first.