Short field technique presupposes that you are not disadvantaged by drag from the runway surface, and therefore willing to allow most of the weight of the aircraft to remain on the wheels longer during the run. With the weight on the wheels, you are not trying to coax the aircraft into the air early, thus it will accellerate faster, and reach takeoff speed in less time and runway length. You don't have the aerodynamic drag of the high lift devices (flaps) and deflected elevator trying to pry the nose up early in the takeoff. The short field technique also usually employs a brakes on then full power, then brakes released takeoff beginning. As you reach takeoff speed faster, you rotate on schedule, and you're airborne and climbing as soon as possible over the obsticle.
Soft field technique is based on the premise that you've got lots of space available, but the surface is soft, and getting the aircraft to accellerate to takeoff speed at all is going to be a problem (mud). You will avoid stopping at all if possible from taxi to takeoff, and you will be getting the weight off the wheels as early in the run as possible. You will use more runway length doing this, but you have a much better chance of reaching takeoff speed than carving huge ruts down the runway slowly. Soft field technique will have you off the ground at a low speed, and with less than ideal climb performance until you get the plane cleaned up a little, and accellerating in ground effect.
Soft filed technique is excellent elsewhere too, for example gravel runways, where you are trying to prevent gravel damage to the prop. Get the prop up and away from the gravel as soon as possible. The handling of the aircraft in this way is also more the norm for heavy weight float flying. In these operations, getting one float out of the water first helps immensely. Similarly, getting one of the two mainwheels out of the mud as you accellerate works really well too on some types, but is an advanced flying technique, which requires practice.
Aggressive soft field technique can get you in trouble in some types (PA28) where the aircraft will get airborne, then stuck flying in ground effect. It can be very dangerous in a confined area, and thus, again soft field technique requires training and practice in the aircraft type involved. Some types are nearly useless at soft field ("T" tails) as you just cannot get the pitch authority early enough in the roll to create much beneficial affect.
I hope than helps, Pilot DAR