Perhaps the most common carrythrough today is the carrythrough raiz. In this scenario, we land in a hyper stance, or by extension, a hook trick or katana. The hips turn to face the direction of momentum, then the in-air leg is swung into a clear frontswing, initiating the raiz or cheat trick. The key to efficiently generating power in this transition is to allow the energy of the preceding trick to essentially drag the hips and base leg through the stance change, before or while utilizing an intentional, powerful swing. Certainly pivoting before initiating the swing is easiest, but it is possible to seamlessly blend both parts into one fluid movement.
As mentioned, this sort of carrythrough is often understood as the only carrythrough for many trickers, however that mentality is quickly dying off.