Mechanical
Several anemometers use physical moving parts to determine the wind speed. The cup anemometer uses a number of hollow cups, typically three, on the end of short poles arranged on a horizontal axis. The wind catches the hollow cups and the wind speed is determined by how fast the anemometer turns. A similar anemometer uses a windmill or turbine design. Shaped blades arrayed on a vertical axis are pushed by the wind, allowing the speed to be measured. Mechanical anemometers are generally cheap and easy to install, except for the larger windmill or turbine designs.
Electronic
Not all anemometer use moving parts, instead relying on electronics to measure air speed. The hot wire anemometer uses a small thermal prop that measures the amount of cooling provided by passing air flow. The more the probe cools, the faster the air is moving past it. A laser anemometer uses a laser beam directed out of the device along with a stream of particulates. The particulates cause the laser to scatter back to a sensor on the device. Wind speeds produce different effects on the particulates, which are reflected by the scattered laser, allowing speeds to be measured. Sonic anemometers use an ultrasonic wave directed between sensors, the amount of air flow between the sensors affects the wave, slowing it. Electronic anemometers are typically very durable and can measure quick changes in wind speed.
Pressure
Pressure anemometers use either air pressure from trapped air or physical force to measure the air velocity. In a plate anemometer the air flow is deflected against the surface of a pressure plate. The amount of force on the plate is measured, giving the wind velocity. In a tube anemometer air is directed into a roughly U-shaped tube. Inside the tube is a pressure sensor. The faster that air enter the tube, the higher the pressure.
Observation
You can measure wind speed without sensors, using instead observation and mathematics. A windsock is a cone-shaped flag with a hole cut out of one end. Wind catches and fills the windsock, higher air velocities cause more of the sock to fill. A ping pong ball hung from a pole can also be used to measure wind speed by calculating the distance the wind pushes the ball away from the pole. The Beaufort chart, created in 1805, was created as a means of estimating wind speed based on visual observation. It can give a rough approximation of wind speeds up to 83 mph.