To do a strafe jump, you have to run and jump at the same time.
I can only give you the steps on a PS3 (that's all I have) so this is what you do:
On videos where you see them strafe jump, you get NEAR to the edge of the place you want to jump from (if you stand on the very edge, you will have no room to run and it won't work)
Then, you run towards the edge of the ledge, and as you reach the edge (just before the edge) you jump. The momentum from the run, combined with the jump, is called a strafe jump.
I'm sure this is what is defined as a strafe jump, but other members can correct me if I'm wrong.
Hope this helps!
EDIT: I realise I didn't give instructions. Go near the edge, click in the L3 button (to run) and as you reach the edge, keep hold of the L3, pushing it in the direction you're going, then press X near the edge of the ledge. I realise this is quite difficult and hence practice is needed to strafe jump.