How meteorologists measure various weather patterns like tornadoes and hurricanes?

Hurricanes are measured through a combination of satellite imagery, manned flights into the storms, Doppler radar, and ground ad seas surface based observations.

Tornadoes are more difficult because they are smaller, shorter lived, and overall less predictable. Measurements have been made using Doppler radar and ground and ground based probes. Even then, most tornadoes do not have any measurements taken, so strength is estimated based on the damage caused.