To begin with, turning on flats and shallow inclines can be done by just shuffling around one foot after the other, but when you need to make sharp corners whilst criss-crossing up steeper slopes, kickturning is the way forward. It’s best practised on the flat first so that you’re not trying to learn something tricky in a precarious position.
First, take a step or two past the corner itself, this means you end up stepping backwards onto the new line, giving yourself more room to swing your skis around. Start by putting your weight on your downhill foot and make sure you’re secure. Lift up your other foot, then extend your leg out in front of you so that your ski becomes vertical. Keeping your balance and trying to keep it from dragging in the snow, swing this leg around and place it down so that you end up looking uphill with your feet facing in different directions, poles planted behind each foot.