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.
Straight running downhill is mainly a question of confidence and balance. As said before, it is better at first to avoid straight running down a steep slope, because the Skis may go so fast that the beginner is quite incapable of keeping up with them and a fall at very high speed is somewhat upsetting and may temporarily shake your nerve.
Choose a low gradient of about 12 deg. or 15 deg. where you can see the out-run which should be on to level ground or even a gentle rise so that the Skis gradually pull up of their own accord. Soft snow is the easiest and confidence may soon be won in this.
Stand upright or bend the knees, but do not bend at the waist. You should feel as though on springs and you want your weight should be well forward over your feet so that you can keep up with the Skis. Standing in tube or bus, facing the way you are going and not holding on to anything is very good practice at home. You will notice that a bus conductor usually gives with the movement of the bus, so that he is prepared for whatever it does. So with Ski-ing. Look ahead and see what the ground is like, and then suit your balance to what is likely to occur as the ground rises or falls. This soon becomes automatic but it needs thinking out at first.