What are the two factors used to determine climate zones

The two most important factors used to determine climate zones are temperature and precipitation.

Explanation:

The temperature indicates if it's warm or cold, if it has seasons during which the temperature varies a lot during the year or not, and other similar measurements.

The precipitation is the amount of rain/snow that falls in an area during a given period.  It's important to know how dry or how wet that zone is.

With these two information you can determine if a region is dry and cold or if it is hot and warm, during the whole year or just a part of it.