How are north and east compents of the wind calculated, given a wind speed and direction? I have a wind speed and wind direction of an aircraft. I need to find wind component along the true North axis and East axis. 

Can anyone explain me how to do that?

Say wind speed is the hypotenuse in the Right angled triangle and angle is wind direction. How to find wind speed along north axis and east axis?
Simply use trigonometric functions: 

$V_{north} = -V \cos \theta $

$V_{east} = -V \sin \theta $

$V$ is wind speed

$\theta$ is wind direction clockwise relative to the true north (e.g. east is 90°). Note that wind direction is typically given as the direction from which the wind is blowing. If you have a wind direction that in given into the direction of air flow, then you should remove the minus signs from the formula's above.