This one is worth stating plainly because the mistake is so common, and because getting it wrong is more awkward than doing nothing at all.
What people actually do#
A handshake in any formal or business setting. Chinese handshakes tend to be lighter and held slightly longer than the firm Western grip — do not squeeze, and do not read softness as disinterest.
A nod and a smile in casual settings. Greeting a shopkeeper, a hotel receptionist or someone you pass needs nothing more.
Nothing physical at all is completely normal. China is not a greeting-by-contact culture; hugging or cheek-kissing someone you have just met will be endured rather than enjoyed.
Where a slight bow does appear#
A small forward inclination — more of a deep nod than a bow — shows up as a marker of respect or thanks, often paired with a handshake toward someone notably senior or elderly. It is a modest gesture, not the formal bow of Japanese practice.
Follow rather than initiate. If someone inclines toward you, return it. Do not open with one.
What to say#
你好 (nǐ hǎo) works universally. 您好 (nín hǎo) is its respectful form, worth using with anyone older or senior.
You will be asked 吃了吗 — "have you eaten?" — which is a greeting rather than an invitation. Answer yes and it has done its job.
The gestures to avoid instead#
Beckoning with an upturned finger is rude; wave with your palm down and fingers together. Pointing at people with a finger is impolite — use an open hand. Neither is likely to cause offence coming from an obvious foreigner, but both are easy to get right.
For seating, gift-giving, hosting and the conventions underneath all of this, read the guide to Chinese etiquette.