motoadve started a good discussion about tricycle gear takeoff, but we all got bogged down in the mud and never answered his question: "Tricycle gear, what is the your technique for short field takeoffs." The basic low ground effect takeoff is the most efficient takeoff on any surface with either tricycle or tail wheel airplane.
So to answer motoadve's question, I use the basic low ground effect takeoff on all takeoffs except ITO.
Until off the ground, this is the old soft field takeoff procedure. Because the center of gravity is in front of the main gear, the nose wheel is heavy. Also, any mitigation of the forward movement of the main wheels levers extra weight onto the nose wheel. There is some mechanical friction mitigation of the forward movement of the main wheels on any surface. This wheel barrow effect must be dealt with initially with full back stick and full prop blast on the elevator. Still a problem in snow, grass, mud, etc., but that is the best we can do. A safety feature, in a muddy condition like in motoadve's video, is that we will know pretty soon if we can't get off. If the nose gear does not come up out of the mud, we will not get off. We can stop right there.
Like Cary said, the common error with this soft field as a short field technique is that once off, we allow the nose wheel to come way off in a very high pitch attitude. This high pitch attitude mitigates acceleration dramatically. We need to keep the nose wheel just off or rolling without either aircraft weight or any lever action pressure from the friction on the mains.
Now that we have the nose wheel just off and have accelerated enough, we want to use the elevator again to pitch up and get the mains off. Anything on the surface (nose wheel, mains, skids, skis, floats, anything) will lengthen the takeoff run. The design of the airplane is to fly, not move mechanically on the ground or sail in the water. Yes popping the flaps rather than using the elevator will work, but both flap and back on the elevator work best. If we pop the flaps, we want to do it early. If it doesn't pop right up, we need to use elevator as well. We will be wobbly but we need to get the mains off as soon as possible. We're not going for pretty, we are going for the free, extra ground effect kinetic energy.
A very common error, at the point where the mains come off, is to allow the airplane to climb out of low ground effect and get mushy. To get comfortable with pushing hard to get the nose level quickly, in low ground effect, I have students get comfortable with gross dynamic for/aft control wheel movement first. Too often pilots go for the "hover button" first and are just too dammed late. Push the stick forward hard. If you don't like what you get, pull it back. Etc., etc.
The most common error is to go to a high pitch attitude at Vx or Vy airspeed, on a instrument inside the cockpit where our eyes should not be, as now appropriate in the PTS. At least the FAA now admits that we need to accelerate in ground effect. Every extra second we can stay in low ground effect is extra, free kinetic energy of pressure airspeed that can be traded for altitude WHEN NEEDED AT THE OBSTRUCTION.
If the departure path is curved and we don't yet have enough airspeed to safely climb up to clear the down wing in the turn, we can make the wings level rudder turn. Cross controlled? Yes. Creates more parasite drag? Yes. Works safely? Yes.
The tremendous lift, speed, maneuverability, advantage of the free, extra kinetic energy of ground effect is almost unknown in aviation outside of crop dusting. Crop dusters have millions of hours operating overgross because of this free, extra energy. On takeoff, we need to get it as quick as possible and keep it as long as possible.


