Most of Chinese idioms are from old stories. The words graphically show the meaning of the idioms. Here are some examples:
wànɡ méi zhǐ kě
望 梅 止 渴
This story is: One summer, Cao Cao was leading his army in a punitive expedition against Zhang Xiu. It was very hot. The soldiers were walking in a mountain. They were so tired and thirsty that they wouldn't want to move anymore. Cao Cao was very worried about the walking speed. After thinking for a while he had an idea. He came to the head of the army. He said, "Soldiers, I know there is a big forest of sour plums in the other side of the mountain. The plums there really delicious. Hurry up！" When the solders heard this, they were so excited and imagining they are eating the plums .They walked faster and faster.
望wànɡ means thinking of. 梅méi means sour plums. 止zhǐ means to stop. 渴kě means thirsty. Now the idiom is used to describe doing nothing but day dreaming.
Here are some frequently-used Chinese idioms:
笨鸟先飞（bèn niǎo xiān fēi）:A slow sparrow should make an early start.
心想事成（xīn xiǎnɡ shì chénɡ: May all your wish come true.
后生可畏 (hòushēng kě wèi)：It is used to describe young people are excellent and can exceed their elders and make others stand in awe.
后生( hòushēng )refers young people.
十全十美(shí quán shí měi): be perfect in every way
车水马龙(chē shuǐ mǎ long): incessant [endless] stream of horses and carriages
You can learn more Chinese idioms or sentences here.