Posted by Wolfenstein
Jackelope explained it pretty well--I know their are some fundamental differences in different schools.
I'll just focus on the rear low kick, and how it is taught in my school.
You open up your hips by stepping out with your front leg--this will chamber your kick and give you a wider angle to swing from--the knee can be slightly bent, but for the most part it is straight. Assuming you're orthodox --you will use your right hand to counter balance, which we call the slice--so your right hand drops and makes a slicing motion, helping you to regain your balance and reset. Think of it like swinging a bat, or sweeping with a broom. You want to aim your knee as close to the target as possible, and ideally land with the shin, and at worst the instep.
Way to expound on the kick even better Wolfenstein
That initial step to open the hips is the key. Remember that step should always be stepped outside the stance of your opponent. Not only does this ensure you'll achieve maximum power, but it places your head off line for the counter punch (assuming you're orthodox fighting an orthodox fighter, a straight right hand AKA 2 shot will almost always counter the low 10 aka low round, so you've GOT to move your head in order to not get James Irvin'd) Also, step onto the ball of your foot when you do this, and make sure that you turn your planted heel through with the kick