Depends what kind. Chinese school in china would just be called a school, or 学校 (shue shiao). A Chinese school abroad that receives funding from the Chinese government is probably called a 孔子学校 (kong zzz (like the zz in buzz) shue shiao)
To say "I speak Chinese" (in Mandarin) you say: Wo(3) hui(4) shuo(1) Zhong(1)wen(2). 我会说中文. To say "You speak Chinese" you say: Ni(3) hui(4) shuo(1) Zhong(1)wen(2). 你会说中文. You can...