When you have begun to feel at home on Skis, go off to a much steeper slope and try traversing. Choose a slope which has flattish ground below so that you have an easy out-run and nothing to make you nervous.
Remember for your comfort that if you go across a slope leading with the upper foot and with most of your weight on the lower foot--standing upright and, if anything, leaning a little outwards away from the slope, you can traverse across almost any slope without difficulty, so long as it is not too steep for the snow to bear your weight without slipping itself. Nothing is more comforting to a beginner than to realize this. It takes away the feeling of giddiness and gives confidence, but it needs learning and should be practised at once.
The first tendency of Skis on a steepish slope is to point more and more downhill till, finally having intimidated the beginner into allowing them to go their own way, they plunge straight down, and the beginner collapses. To counteract this put more weight on the heel and less on the toes while traversing.
This will push the back part of the Skis down and the front part uphill across the slope and, if done sufficiently, the Skis will stop and you have begun to get some feeling of control when traversing.
Standing upright the inner edge of your Skis will bite into the snow. Try leaning inwards, as you will do by instinct, and you will find your feet slipping away down the slope and you will gracefully recline full length against it. It is exactly the same when walking across a steep grass slope in Summer. Most of the slips are due to leaning towards instead of away from the slopes.
As you get more confidence in your running, try lifting one Ski off the ground as you slide along. Or even take off one Ski and try running on the other; lifting a Ski will often save a fall. For instance if the Skis get crossed, just lift the upper one and put it down beside the other again while running. It is perfectly easy and yet I have known people who, after weeks of practice, dared not lift a Ski off the ground while moving, only because they had never tried it as routine practice.
Whatever you do by way of practice do it first on one foot and then on the other, or you will become a right or left-footed Ski-er and it will take ages for you to feel equal confidence in either foot. This applies especially to turns. Beginners will often go on practising a turn on the right foot, till they can do it and then have to re-learn it completely on the left foot.