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I have an Ac to Dc switched-mode power supply that looks a bit like this : 
Now as you may or may not know, there's the Ac input with a N and a L for neutral and live line. Now I want to know if it's ok to plug the Live line on the neutral side and vis versa. Also how am I capable of knowing wich of the wire I connect to it is the Live or Neutral line. Now I've also been told not to do this, thanks for explaining me why is that..
simulate this circuit – Schematic created using CircuitLab
One good reason to do this is that the internal fuse will be on the L terminal. This is somewhat safer because if the fuse blows the power-supply is internally isolated from the mains live. If the fuse blows when wired the other way around then the internal circuitry is still live and the neutral is disconnected.
In many countries the plugs are non-polarised and can be inserted either way around. This means your L and N are swapped. There is nothing you can do about this.
You'll be fine either way. Do connect the earth!
Links to my other answers on related topics:
You can safely swap Live and Neutral.
In my region (mainland Europe) the plug that we use to connect to mains is symmetrical:
So it depends on how you plug the connector in the socket if Live and Neutral are swapped or not.
If that mattered that would be very dangerous.
So it does not matter, on such a supply live and neutral are treated equally, the names are only used because that's sort of a standard.
In practice the Neutral often is not even neutral but can have a dangerously high voltage.
What is more important, since this supply has a metal case is that you ground it properly. That means connecting the ground from the mains socket to the supply. So using a 2-wire mains plug is no good ! You need to use a 3-wire mains plug.
Almost certainly the supply treats the line and neutral inputs symmetrically. You should in theory be able to swap them, but of course you should always check the datasheet. There is probably a spec for the maximum voltage of line and neutral from ground.
The ground, however, needs to be connected correctly. That is important since this supply has a conductive case.
In US house wiring, "neutral" is usually tied to earth ground at the breaker box. It is not good practice in the US to swap neutral and hot wires. Chassis should be tied to earth ground, and well-designed devices are built so that an internal short of the hot wire to earth ground will blow the fuse or breaker. If you swap wires, you may be defeating this approach.
Black is hot, white is neutral, green is earth ground.
