Smooth clutch engagement is the first skill to learn. Auto-Union is right on target with his technique. I've taught the same thing many times myself.
The problem noobs have with jerking the clutch is simple physics, by the way. It has to do with the mass of the left foot and leg, and the noob's lack of learned anticipation of clutch engagement and the consequential acceleration and change in acceleration. Basically it's this: as the clutch engages, the car experiences a relatively high "jerk" which is an elevator-industry term for the first derivative of acceleration (the third derivative of position for those counting). The "jerk" causes the car to leap forward, while the noob's left leg and foot are "left behind" (i.e. the car, seat, noob's body, etc. are moving and accelerating forward, but the leg and foot, being hinged and flexible, aren't). Well, the consequence of the lag in leg position is that the clutch pedal is jerked rapidly rearward relative to car position thereby causing rapid clutch engagement. Eventually, the noob learns to compensate for the momentary da/dt and hold his/her leg steady when the clutch first engages, producing a smooth engagement.
Now think about stalling. The exact opposite effect is happening on the throttle. While the left leg is engaging the clutch too rapidly, the right leg, also being "left behind" is closing the throttle at the same moment. Again, with enough practice and learning to anticipate the da/dt, the right foot learns to maintain pressure on the gas to maintain rpm through the period of clutch engagement.
If you think about all of the above, the wisdom of teaching gentle clutch engagement, then immediately disengagement becomes immediately apparent. Repeating and learning to deal with that startup transient is the key to learning to shift smoothly.
I'll leave it up to the interested student to draw appropriate freebody diagrams with all appropriate force and acceleration vectors. There will be a quiz.