Video by kyryllo
Two "versions": Basic and Attacking
Step by Step
1.Turn around till your back is facing the target
2.Bend your upper body down and bring your wieght on your supporting leg, while sticking your butt in the direction of the target
(The basic technique also incluedes turning the head and looking at the target over the shoulder on the kicking side at this point, however experienced fighters tend not to look at all or just glance with the corner of the eye. In reality the foot goes so fast that you have no oportunity anymore to correct the kick, so looking and aiming becomes obsolete. You aim before you launch the kick!)
3.Chamber the leg by bending the knee as far as you can, the heel should point at the target, the knee MUST point down
4.Straighten your leg in a pushing motion towards the target
5.Impact happens with the flat foot or (better) with the heel.
Advanced, Attacking back kick:
Bounce forward to bring the weight above the front (later supporting) leg, at the same time perform the steps 1.-3. simultaneously
Points 4.+5. are obviously the same as in the basic technique.
You may slide on the supporting leg while performing it to gain distance but make sure to have a solid stand at the point of impact.
knee MUST point down, back MUST face the target
head MAY turn around and look over the shoulder
the upper body SHOULD be bent, it improves the stability by bringing the center of gravity down and stops the rotating motion, it also gives you more power since the center of gravity is closer to the force vector and it is simply easier to raise the leg that way. However you can throw the kick standing upright, I wouldn't recomand it though.