To show off with an axe to 鲁班 (Lǔ Bān)
When someone incompetent or unskilled overestimates their abilities and "shows off" to someone who actually is skilled
Negative
他总是告诉上司怎样经营生意，简直是班门弄斧 | Tā zǒng shì gàosù shàngsi zěnyàng jīngyíng shēngyì, jiǎnzhí shì bānménnòngfǔ
He's always telling his supervisor how to run the company. It's like he's trying to a fish how to swim.
[Source]
小华的爸爸是围棋高手，你和他比试，不是班门弄斧吗？ | Xiǎo huá de bàba shì wéiqí gāoshǒu, nǐ hé tā bǐshì, bù shì bānménnòngfǔ ma?
Xiao Hua's father is a master at [the board game] Go. If you compete with him, wouldn't you be making a fool of yourself?
[Source]
Teach a fish how to swim
To make a fool of oneself
None
For beginner students: if you're confused what 门 (mén) is doing in this chengyu, know that it has other meanings besides "door," such as "family" or "house" or "school."
Apparently another English equivalent is "teach grandmother to suck eggs," but I've never heard that in my entire native English-speaking life, so I'm not putting it down
《王氏伯仲唱和诗序》(Wáng Shì Bó Zhòng Chàng Hè Shī Xù) by 柳宗元 (Liǔ Zōng Yuán), a Táng Dynasty (唐, 618-907) essayist and poet
In the Táng Dynasty (唐, 618-907), there was a famous poet named 李白 (Lǐ Bái, 701-762) who drowned after becoming intoxicated and falling into the Yangtze River (长江, Cháng Jiāng). Eventually, his tomb and the surrounding areas became popular tourist attractions, and many tourists, including some scholars, would carve poems onto the surface of 李白's grave and the other scenic spots.
Several centuries later, a Míng Dynasty (明, 1368-1644) poet named 梅之涣 (Méi Zhī Huàn) visited 李白's gravesite and grew angered by how it had been vandalized by poorly-written poems. When he returned home, he picked up a brush and wrote his own poem mocking those who had dared write for 李白. In the poem, he indicated that leaving poems for a renowned poet was like "showing off with an axe in front of 鲁班 (Lǔ Bān)." 鲁班 was a famous carpenter from the Spring and Autumn Period (春秋时代, chūn qiú shí dài, 770 - 476 BC). People claimed that he was the best in the world, to the point that they regarded him the father of carpentry, and so when anyone claimed they were better than him, they would laugh and scorn them for overestimating their abilities.