The strength and gusts are also reported by the tower, they'll say something like "Wind 270 at 15 gusting 25, runway 23 cleared to land" which means the wind is coming from 270 degrees (West), at 15 knots with gusts up to 25. Then you have a general idea of the crosswind on the runway being about 12kt gusting just under 20ish from the right. Accurate enough to figure out whether a limit needs to be calculated.
It's not a precision instrument. Windsocks wear out fairly quickly. It' gives you the direction fairly accurately, and the speed say +- 5 knots, which is adequate to choose a runway and have a good initial guess of how to correct for a crosswind. Once you've started your takeoff/approach, you make corrections based on the observed behavior of the plane, e.g. on final approach, if you drift a little to the right of centerline, you correct a little to the left.