How are north and east compents of the wind calculated, given a wind speed and direction?
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.