My DHT22 module doesn`t work at all
The product page you linked to has modules of different types.
Make sure you have uncommented the matching type in the this section of the example:
// Uncomment whatever type you're using!
//#define DHTTYPE DHT11   // DHT 11
#define DHTTYPE DHT22   // DHT 22  (AM2302), AM2321
//#define DHTTYPE DHT21   // DHT 21 (AM2301)

Also makers of these boards sometimes label them incorrectly or describe them incorrectly when selling them.  If you're unsure what you have, try them all.