The theory behind plasma climbing is quite easy. You set your aim where the wall meets the ground, move the cross hair upwards a few pixels. Then you press 'forward' all the time while standing next to the wall. You jump, and on the way upwards (still keeping 'forward') you start to fire your plasma-gun. During a basic climb you do not need to move your aim (as demonstrated in the video) but rather a straight line upwards.
The most common mistake to failed plasma-climbs is that the 'jump' key is pressed down for too long. Simply tap the button quickly, do not hold it pressed down. Good luck and happy climbing.
I hear you asking if this is useful in 'real-life' scenarios on 'real' maps. Of course it is! Do you remember void4 from Open Arena 0.6.0? Well, that tower was possible to climb with the help of plasma-gun. Imagine the look on peoples faces during deathmatch when you stood up there firing away your rockets at them