There is more than one way to do this. One is to use a small PM motor to generate a voltage that corresponds to wind speed. Another uses a reed switch and magnet to generate a train of pulses whose frequency changes with wind speed.
There is also a "no moving parts" design using heated thermistors, but it's a lot harder to linearize and is influenced by humidity. I have no idea how to build it.
An optical shaft encoder connected to a prime mover monitoring the wind.
Pulses coming from the encoder can be used measure speed in proportion to the wind speed causing the rotation of a prime mover.
I have built one few months ago (the picture). The got the idea from here: http://www.instructables.com/id/Easter-Egg-Anemometer-Wind-Speed-Meter
It worked fine but from about 3 to 4 weeks it stopped working normally. the problem is that the motor I used is not a brushless dc motor, the brushes can't hold continuous 24/24 friction for days and with unstable wind speed... Brushless DC motors can be found in hard drives, but it's hard to take them out and to set in a quick project.
I used a small cheap 3$ analog multimeter. I used it as an ammeter (it's better to use as a voltmeter..). To calibrate it, I went with my two brothers in the car in a calm night, one holds the rotor part out from the window, one drives, and I tell my brother to drive at constant speeds and make marks ...
Nearly same as the no moving parts method using thermistors but you can use filament wire that you have taken out of an old toaster. Voltage divider. One section inside of a windproof but thermally conductive and exposed container, and the other section goes in the narrow part of a venturi tube.
It is not very efficient because you should get the filament wires up well above normal ambient temperature. That can mean up to an amp of current depending on your wires. On the other hand you probably don't need much voltage across them so two volts at one amp might do at only 2watts. Getting a low voltage high current supply is still a possible problem.
You need a high input impedance op amp to amplify the changes in voltage in your dividers center and take your readings from the op amps output. With no wind you set your zero. Then you can blow on the venturi filament and cool it, reducing its resistance and making it drop less resistance. That will give you some sort of idea of where your readings are going to go - and you can use a trim pot in the gain control of your op amp to get your scale about right.
You can do almost the same thing with pressure sensors for a pitot tube setup.
The venturis design can block most of the rain and accelerates the airflow which reduces adhesion by mist as well as acting to amplify the input.
You also have the other side of the hot wire voltage divider in baffled container - windproof but still exposed to mists.
Since you are measuring a differential, most of any mist, frost or other humidity effects SHOULD cancel out.
The wires in the venturi would typically be encased in glass capillary tubes which reduces sensitivity but increases durability of the brittle wires. There could also be more than one set of wires in the venturi. In order to get different averaging the probes can be lighter and heavier to work on different time bases due to their different thermal mass.
And I think you are correct that they are never used as a primary wind measurement device. They are more correctly gust meters and should be teamed with another instrument measuring the average wind speed that they can be calibrated against.
I did miss lots of stuff. I am sure that I am still missing more. Sorry.