To move, use your hips to propel your leg forward while keeping the skin in contact with the snow.
Slide your skis rather than lifting them.
Make sure to keep the skis flat on the snow to take advantage of all the grip of your skins.
When the climb becomes more demanding, activate a climbing aid (placed at the rear of the binding) to relieve the tension felt in the calves and maintain even pressure on the ski surface. (It is possible to use the handle of the ski poles to adjust the climbing aids without bending over.)
When the slope is very steep, make a small backward movement with your skis to check the grip of your skins on the ground. This way, you will straighten the hairs of your skins as much as possible, which will give them a better grip. You should also avoid putting your weight too far forward because your skins could come loose. Straighten your torso and move your weight towards your heels.