Turning is generally more advanced, but it can be broken down into four groups
Glutes, Lumbar, Chest, and Pecs.
Glutes
this is one of the main categories for turning. it allows you to block your momentum and turn it to the side.
Lumbar
This is your counterbalance joint. every time you block with your glutes, you'll need to adjust with your lumbar to make up for your excessive lean. this is also a helpful tool while turning.
Chest
Your chest will be your finite turning control center. used mainly for little corrections and to get the most out of your turn, as it's powerful and doesn't need many frames to turn you. use it sparingly and when it's needed. many people will use this joint to counter balance, and that's the wrong use of this joint.
correct uses
For correct uses of the chest, use it in situations where you need power for a specific move. as it's the most powerful joint on the tori, you can gain a hell of a lot of power off one leg when you use it correctly.
Pecs
the last group, this set of joints helps as a counterbalance and turning aid when you attempt a turn. they're great as a shoulder/pec pair because they help with your right/left balance, and aid in turning when used in the right setting.
although in theory turning is easy, executing a smooth turn takes precision, timing, and a really solid knowledge of your tori. a basic turn will consist of about four steps: first step, second step and counterbalance, third step and power turn, and fourth step and completion.
in the above example, a 90 degree turn is executed in a short period of time. notice that the glutes are extended more than usual.
In this example, a smoother and longer turn is applied. the shorter steps, less use of glutes, and minimal lumbar movement create a more upright and looser turn.
notice how zubin has already started his turn before he's even begun running. zubin also stays away from his lumbar, and uses glutes to block more efficiently than i do.
First step
In this step, your farthest foot will begin the block. Depending on what way your want to turn, you'll have to adjust these steps to match. For a left side turn, you'll want to begin your turn with your right leg, and vice versa.
Notice how in this step you can extend either the left or right glute, as long as your furthest leg is the one going away from your body.
Second step
This step consists of countering the lean you'll now most likely have. a couple good ways to do this is to carefully bring your glutes together, while abusing the grounds physics by playing with your ankles and allowing just your toes or heel to hit the ground. this allows for a good pivot point, and once you feel more adjusted, you can play around with how much you raise your toes before you go flat footed.
This step is one of the more crucial ones, as it'll be the step that ensures you keep up on your feet. it's important to remember that this step will lead you into the next slight rotation of your tori, so it's vital that your balance is stable before your next foot goes out.
Third step
This is the one that gets you the most rotation. it's similar to the first, except now you should already have enough lean to continue in the same direction you're traveling in. in this step, make sure that you've got a good block on the ground before transferring your weight to the middle of your body. with a tori turn, you should never have your entire weight shifted to the outside foot. it should rest cleanly on either the inside/middle of your turn, or on the middle of your turn.
Fourth Step(ending step)
this step will be your ending portion. most likely this will be the step with little rotation, so make sure you've gotten sufficient turn from your previous three steps. this step is purely to correct your balance and begin moving in your desired direction. during this step your weight should be over your inside leg, as your motion will probably try to take you over to your outside leg. if that happens, your turn will fail and you'll end up on your side. your previous momentum will probably try to carry you to the side more than forward, so it's essential to keep your weight in a position that is easily manipulated.
After you've stabilized yourself during this step, you're safe to continue running. keep in mind that you won't be perfectly stable after your fourth step, so adjustments after your turn will definitely be needed.