Luckily there's an easy way to work it out, close enough anyway. You don't need any fancy charts, computers etc.
Suppose the wind is reported as 12 @ 350 and runway is 31.
First work out the relative bearing. RB = 350 - 31*10 = 40 degrees.
Now xwind component = wind speed * RB/60, i.e. 12 * 40/60 = 8. If RB is >60, then x-wind = wind speed.
This is as close as the reported winds are ever going to be accurate anyway, and dead easy to do in your head. Worst case error is about 15%.
Not sure about other people, but I found that a confusing explanation of the clock code I explained earlier - and in reality you only need the 15/20/30/40/45 degree off ones which are the easy ones to work out - anything below 15 degrees off is not normally worth worrying about, and above 45 degrees I would work out the 45 degree amount and estimate from there, knowing that at 60 degrees I am looking at full Xwind.