In a natural environment you can have a variety of possible inclination angles, and this even on the same descending route. So it may be necessary to use different technics.
My guess is that the term ‘extreme downhill’ may have different meaning for different people. In any case, this can be descending without tools and with tools.
So what is the best way to walk in extreme downhill? In my view, there are at least three basic types of walk that you can use to walk downhill:
- Scramble by going downhill.
- Descend directly by going side-wise.
- Descend in a switchback style.
These ways are described in detail below.
Some aspects of this question are covered in my separate text about descending a dry grass slope with serious inclination and exposure. The main difference of this text here is that it applies to any kind of surface which you may have while descending.

Scramble by going downhill
Perhaps some people are more used to use the term scramble for ascending, but the same technic must be used when you descend on extremely steep sections.
This is presented in the sketch below. Basically, you walk backwards and you face the ground in front of you.

So this is a way for extreme situations. It is always easier to scramble up than down because you can see better what is above you than what is below you.
It may be hard to see where to put your foot, and also to judge properly if the place is stable enough to keep your weight. A partner below you might help in navigating you at such passages.
With tools or without tools?
If you are on such sections, it is a must to have free hands, so forget your trekking poles and attach them to your backpack. This would mean going without tools.
However, if you have an ice axe, you might need it sometimes, so have it ready. This can be if you realize that, in order to put your foot in a safe position, you still need a few centimeters even if you extend your body to its maximum.
Such sections are also dangerous because you can push some unstable rock and this may be bad for people that are possibly below you. You yourself can be in danger if there are people above you.
So at such places use your helmet if you have it. It may help also if you fall, you never know. Going roped over such a terrain is also a good idea.
Descend directly by going side-wise
This is a situation when the downhill route is very steep, but still less steep than in the scramble case described above. So you have no space to go switchback type, and you have to descend directly. This is shown in the sketch:

The weight is almost all on your lower leg, and you will feel this. Your muscles may tremble after some time. This is why it is good to turn occasionally so that you can use your less tired leg.
In such passages, it is good to have tools. Both trekking poles and an ice axe will be of great help. My preference would be an axe because you can use it for self-arrest if you fall. You should keep it in the up-hill side hand all the time because it is too short to be used on the down-hill side.
If you use poles, in my view it is best that straps are not around your hands. This is because if you fall, you will need hands for self-arrest and this can be difficult with poles dangling around you.
Regarding helmet use, the same applies as in the previous case, so use it if you have it.

Descend in a switchback style
This is for the mildest of the three situations presented here. This implies that you have a slope with an area wide enough to go zig-zag and to navigate it downhill in the safest possible way as illustrated in the sketch below.

This is good also because your down-hill leg, which is exposed to more force, is not always the same. According to a study on prevention of muscle damage, such prolonged downhill walking may induces damages to leg muscles and it may reduce force generating ability and muscle coordination. These all increase risks for more serious injuries.
On such passages it is very good to have poles, both for balance and also to help your knees. I mentioned this also in my post about uphill and downhill walk comparison. If you descend with an ice axe in your hand, keep it on the up-hill side.

How about other people around? Well, see the photo below, this is from one of my tours in the Dolomites in Italy, and this is a switchback type passage.
As you realize, the slope is steep enough to have danger of rocks destabilized by people above you. So keep an eye on what is happening and react accordingly.

How about body posture?
I have seen a variety of ridiculous advises regarding straight posture, upright torso, bent knees, etc.
This all makes no much sense. You body posture will change all the time, this is dictated by the terrain and not by your desire. You have to adapt to the environment, as simple as that.
Stable foothold
In all the situations described above, this is essential. In the first scenario, you may not see sometimes where you put your foot. This is what makes it dangerous.
In the second and third scenario, you can see where you step. So try to avoid scree and lose surfaces if possible, choose some natural small ledges, stable flat rocks, compacted ground, etc.
If there are animal trails around, you can use them at least partly to navigate some passages. Trekking poles do help, they are good for stability, it is better to have four points on the ground than two. Watch alpine goats and you will realize this.
In any case, it is easier to fall when walking down a slope than walking uphill and you can find out why this is so if you follow the link to may another text.
Summary
So this is more or less all I had to say regarding this topic of walking on extreme downhill. Inspect terrain and choose the safest passages with the mildest descend angle and with a stable ground. This may not always be possible, so apply some of the advises mentioned in the text.
I am sure there are things that may be added here, so let me know, there is a comment box below. Check also my text about drying your socks when hiking and backpacking as well as about ways to dry your boots. Thank you for reading.