During the Stone Age, people in China lived in small villages and had big men in charge, and then chieftains. But by the time of the Shang Dynasty, about 1800 BC, China was united into an empire and there was an emperor or empress who ruled over many smaller kings. Under these kings were a bunch of less powerful lords, and these lords ruled individual farmers. The lords collected taxes from the farmers, and passed some along to the kings, who passed some along to the emperor.
Under the Ch'in dynasty, about 200 BC, the emperors managed to get a lot more power and control of the government. Instead of letting local kings run local government, Ch'in sent out governors and judges that he had chosen himself, who were loyal to China and not to the local king. During the Han Dynasty, the emperors began to use examinations to choose the smartest men to be their governors and judges (they lost out on a lot of good governors by refusing to pick smart women though).
To find out more about ancient Chinese government, check out these books from Amazon.com or from your library:
Eyewitness: Ancient China, by Arthur Cotterell, Alan Hills, and Geoff Brightling (2000). For kids.
Negotiating Daily Life in Traditional China: How Ordinary People Used Contracts, 600-1400, by Valerie Hansen (1995).