Suck up in Chinese is 拍马屁（pāimǎpì）. It literally means to slap horse buttocks. 拍（pāi） means to slap, 马（mǎ） means horse, 屁（pì） means buttocks.
Slap horse buttocks? Why?
This saying comes from the time of Gengis Khan when horses were popular in China (Yuan Dynasty). People would greet each other by complimenting their horse, slapping it on the hindquarters and saying "good horse". It was especially important to tell a boss or official that he had a "good horse" even if the horse wasn't very good. Gradually, this respectful greeting became just a way to flatter a superior. Eventually, when people no longer rode horses all the time, people who complimented their boss insincerely were, in a way, telling their boss they had a "good horse" and figuratively slapping their boss's horse on the buttocks.
Of course, "pāimǎpì" is not unique to Chinese. There are similar sayings in many countries, like America, where people also call this kind of behaviour "buttering someone up".
Here are some examples using this phrase:
Tā zǒngshì xǐhuān pāi biérén mǎpì.
He always likes to suck up to others.
Michael zǒngshì pāi lǎobǎn mǎpì, suǒyǐ dàjiā dōu hěn tǎoyàn tā.
Michael always sucks up to the boss,so everyone hates him.