The Strafe-jump is a main jump in a game and it’s quite easy to perform. Just press strafe (+moveleft/moveright), forward (+forward) and jump (+moveup) buttons simultaneously or just strafe and forward, and then jump.
Base strafe-jump. Other kinds of jump derive from it. Base strafe-jump is explained on strafe-jump on q3tourney4 in a room at the second floor with a view on the Railgun. Come up to health and look at the wall before you or at the jump-pad but not at the place you are going to jump at. Go forward (+forward) and then at the edge of the platform press strafe to the direction you need and jump (+moveright and +moveup/+moveleft), holding forward (+forward) at the same time and turn your head in the direction of your jumping. The secret is in the turn of the head for it gives acceleration. That’s why you shouldn’t look at the jump spot from the very beginning in order to look at it later.
Jumping about is the most useful kind of strafe-jump. It’s a truncated variant of the strafe-jump, the point of jumping about is that a head turning isn’t very important here, it’s used in very truncated way - just for starting off. Jumping about implies two or more strafejumps, and left and right jumps go in turns, though you can make them only in one side. You can speed up you moving around the level by means of jumping about.