Nowadays cupping hands is only commonly used during New Year's Day
Hands shaking, as a courtesy, was introduced to China just decades ago. It is still not quite commonly practiced in the rural areas of China. Even if it is popular in the urban regions, you will find hands shaking in China is not naturally adopted. Most Chinese still don't know when to offer their hands, how to hold the offered hand, and for how long to hold the offered hand. You will often find only your fingers are lightly held or touched to be exact. Or sometimes you will find the Chinese will not offer their hands at all when they are introduced. Instead, most likely they will make a nodding or slight bowing. Of course, they won't bow to their waists as the Japanese do.
Traditional Chinese courtesies equivalent to hands shaking are kneeling (The Chinese use "kowtow") and cupping one's hands before one's chest. In the past, children used to kneel before their parents every morning to pay their respects, and the magistrates to the emperor. Nowadays, when people express their deep respect or gratitude, they will still kneel. As for cupping hands before the chest, people sometimes use this gesture and at the same time with the expression "Glad to meet you. (幸会幸会 Xinghui xinghui.)". Cupping hands is also often used when you greet people on New Year's Day with an accompanying expression "Wishing you good fortune. (万事如意！Wan shi ru yi!)".
Excerpt from: Chinese Culture Pictorial
By: Cathy Xiaoxia Zhou
Editor: Ding Yujie