Get in an airplane and fly up to the base, then the top. Other wise, I know of no accurate way. You could use some type of sextant type angular measuring device, I guess, if you also know the exact distance to the cloud.

I am more interested in what type of clouds they are, and which way they are moving, and what's causing it. Sea Breeze? Cold Front? Building Thunderstorm?

I like to see the big picture (on the Weather Channel) and then allow for the local geographic influences which will affect the surface wind.

Remember, Bethwaite was also a competition glider pilot, so he was very much interested in updrafts/downdrafts, etc. thus his focus on cloud heights.