They speak both languages. Most Chinese people speak Putonghwa(Mandarin).

Foreigners pay big bucks to learn Chinese. Ussually about 100 yuan per hour. However, there are some schools that offer packages, but the prices are high. You can always use the Berlitz CD and book set.

Sometimes the school you teach English at will offer to give you free Chinese lessons. Tell your supervisor that you want to learn Chinese, they are ussually happy to set you up with learning their language.