In what would be a great project to demonstrate part of the process of measuring weather data, Instructables member hansverkaik has documented how to make a classic hygrometer - a device to measure the amount of relative humidity in the air.
This process uses two temperature sensors, one to measure the dry air temperature and another in an enclosure to measure the wet temperature. With this data the humidity can then be calculated by an Arduino or compatible and displayed on an LCD.
If you're looking for a sensor to measure temperature and humidity - check out our HUMID: humidity and temperature sensor module. Designed around the DHT22 sensor, it only requires one digital pin and power - and is easy to use with out Quick Start guide. With a temperature range of -4°C to +125°C with +/-0.5°C accuracy, and humidity at 0-100% with 2-5% accuracy you're ready to measure. For more information and to order, click here.