there is no 'best" way to ski ice, there is a best way to ski though.
Everything I am going to mention is stuff that we should be doing on on almost all snow types its just that the more forgiving conditions make us forget about them.
The biggest rules for skiing that become unbreakable on ice are these.
Balance on your outside ski early in the turn.
Turn shape is round whether its skidded or carved
you are countered to the turn which helps keeps pressure on your outside ski IE hips face down the hill
You are always 'moving" with the turn.
there are tons of things you could be doing that is preventing you from skiing ice and there is also a chance that your skis are just not good on ice but it it technique related I am a betting man and I bet its one of those 4 things I mentioned. Ill explain each a little further.
Balance on your outside skis is key, and its also something that alot of PSIAer seem to be confused on because of the talk of a strong inside half. balancing on our side ski is a by product of the other 3 things mentioned. If your always moving with your turn, if your countered, and your turn is round AND your shortening up your inside leg the appropriate amount for the turn it would be hard not to be balanced on your inside ski.
drills - Javelin turns, dynamic wedge turns, skate to shape, and skate to shape while doing dynamic wedge turns.
Turn shape is round skidded, scarved, carved, arc I do not care which you call it but your ski has to be cutting the snow. Think of is like butter knife in a butter. If the knife is vertical placed into the butter it is not going to be easy to move but if it layed on it flat side it easier to smear. You want to knife to vertical and not easy to move for purpose of out skiing. Patience and not rushing anything is key for this to happen, the natural sidecut of the ski should be used to assist with the turn shape. The moment you start to rush things is when sideways uncontrollable to mere advanced skis happen.
drills -patience turns, funnel turns, follow the leader with a skilled coach
Counteered to the turn, by this I mean that your hips are level and that they are mostly facing down the hill if on really icey terrain excessively so. The easiest way to accomplish this is to pull your inside hip up and forward in the turn. It can be hard physically to do this turn after turn if your not use to it.
drills - target practice, hiesmen drill, the fall LINE drill,
moving though the turn. Simply put skiing is a dynamic balance sport and to balance dynamic we always have to keep moving. In the context of skiing are movement are forward and for anglanol with some delays happening in high end skiing ie foot squirt. Let forget about the foot squirt and talk about the basics. From our first straight run to to the first turn, to skiing tree aggressively we are always moving trying to keep our Center Of Mass with our skis. To do this we need properly fitted boots and binding that do have a proper delta angle for the skier. Once that it taking place simply driving our knees and hips forward though ankle flex is how we accomplish this.
drills - low end - thousand step straight run, thousand steps witih toes on the ground straight run, straight line shuffle
mid end - skate down the fall line, thousand step turns,linking turns while lift up your inside skis heel, shuffle turns easy terrain
high end - the fall LINE drill, skate to shape turns
these will all help ski ice better, but at the same time we as skier should always being doing these movements all the time anyways.