There are many interpretations of the concept 'wuwei' which is translated as 'non-doing' or 'not doing'. Let's examine some of these ideas for reflection purposes.
Seclusion?
At the level of personal action, some people seem to think that this concept refers to seclusion. The idea of just observing the world without acting in it, sort of being above or beyond it all. They could easily get the idea that by going into seclusion and hanging out on a mountain all day they will become one with the Tao. Seems like a fair interpretation, however, it is important (although only relatively so) to realize that the Taoist mentality is not to separate themselves from the world or from worldly affairs. Check into chapter 4 of the Zhuang Zi to confirm that:
Nothing is as good as following orders (obeying fate)
For some time in one's life it may be beneficial to live in seclusion and many Taoist masters have done this. But this is certainly not a requirement nor is it related to the idea of 'wuwei'. When in seclusion, what do you do? The idea might seem appealing but the existential questions cannot be answered by changing one's location. This is looking outward for an answer that can only be found inside.
The Way is always uncontrived
yet there's nothing it doesn't do.
If lords and monarchs could keep to it,
all beings would evolve spontaneously.
When they have evolved and want to act,
I would stabilize them with nameless simplicity.
Even nameless simplicity would not be wanted.
By not wanting, there is calm, and the world will straighten itself.
Passivity?
Often enough, people will confuse Taoist philosophy for one of passivity|passiveness. Not doing anything, dropping all responsibility and leaving everything unattended. If that were true, then how could a Taoist live an thrive? Many Taoist masters will happily heal the sick, tend their garden, help someone carry their groceries or work at the supermarket. They will perform all these activities (do all these things) while in a state of 'wuwei'. No, the Taoist is not passive, an whatever they are doing is not related to 'wuwei'...
The Tao is constant in non-action
Yet there is nothing it does not do
Following the laws of nature?
Then there is this idea about following the laws of nature. According to this concept, a Taoist studies nature like some scientist and observes life to understand the ideal natural circumstances for things to take their optimal path. Like how you would plant a certain bush in accordance to it's optimal sun exposure, ground composition etc and just give it the right amount of water when it seems to dry out a little. And through mindful observation one should evolve towards doing these things in a way that is most effective and efficient so as not to waste any effort.
Hmm - no. A Taoist will certainly observe and naturally gain a certain know-how. But to study nature and to analyze and formulate these observations into laws is not the Taoist way. Nature will do as nature will do. A Taoist will do as a Taoist will do. But the laws of nature are not related to 'wuwei'...
What is this thing called the Way? There is the Way of Heaven, and the way of man. To rest in inaction, and command respect - this is the Way of Heaven. To engage in action and become entangled in it - this is the way of man. The ruler is the Way of Heaven; his subjects are the way of man. The Way of Heaven and the way of man are far apart. This is something to consider carefully!
Doing non-doing
Wei wu wei - 'doing non-doing' is exactly what it says - the only thing you're doing is - dropping any activity that you can relate to yourself. Thereby removing your identity from the perceived reality, and arriving in 'wu wei' - not-doing. Just being.
In practice: Whatever is being done right now - examine who is doing it? If it is you - stop doing it. Continue looking for things that you are doing and stop doing them also. When all is gone - stop looking for things, as that is something you're doing as well. Now you have entered the 'wuwei' state.
When in 'wuwei', things are being done. But it's not you who's doing it. You are not even there - so how could you?
Related article - Forget about everything.