Balance, Edging, Pressure are the basics. PSIA used to use "BERP", but as carving skis have become the norm 'rotary' is less emphasized (but still a skill).
Balance: A good stance, feet about hip width apart, ankles flexed so that the hips are over the feet, hands in a comfortable position, shoulders relaxed, eyes ahead.
Edging: tipping the skis on their sides to engage the edge(s).
Pressure: downward pressure onto the ski via a balanced position, which increases the bend in the ski, which, combined with edging, creates the turn.
Everything else is fine tuning, but those are the core basics. If you are missing one or the other, you will struggle. The USST is focusing heavily on this with their BASE test system, and PSIA is following suit also (albeit slightly differently).
Balance is the most important above all.