Skid vs Carve
When we want to skid a turn, we twist the board torsionally, think of grabbing the tip and tail and twisting opposite like wringing out a towel. Now do this with your feet, pull up on your left toes while pushing down on your right toes. This is torsional twist, and any time we do this we skid our turns (and is a very good habit while trying to make skidded turns.
Carving, on the other hand, we do with no twist at all, but instead we tilt the board on edge. We do this using our ankles moving together, ex: pull both toes up equally until the board tilts up on its edge....
To try this for the first time, start in a slightly downhill traverse, and try to tilt the board up on its edge by moving both ankles at the same time and balance along the effective egde (you must have some speed for this) Remember to keep your knees bent and eyes up, once your on your edge the board will be turning (though not a tight of a turn as your used to in skidding) and just hold on to the tilt, and the turn, until you start traveling up the hill to a stop. Look back at your track, is it one smooth line? if so great keep practicing.
If not, try again focusing on keeping your upper body very calm, and in line with the board. Just using your lower body to tilt the board onto the edge and "hang on for the ride", in other words, dont try to turn harder than the board is already turning, just keep riding that edge. In a carved turn we can only control our speed by staying in the turn until it carries us across or even back up the fall line. Try one edge all the way to a stop, then the other, keep trying til its smooth and comfortable every time, then try to like them together...
Good luck
Oh i almost forgot, on toe side our ankles are flexed, we are not extending our ankles and standing up on our toes, instead bending our knees, and putting tons of pressure on the shins of the boots while allowing your ankle to flex (or collapse if that makes more sense) is the way to smooth toeside turns. This is true for skidding or carving