1. Explain it simply
Verb + 一下 means 'do it briefly / for a moment' (看一下 = take a look, 等一下 = wait a bit).
The order is Verb + 一下, never 一下 before the verb.
It makes a request sound softer and more polite.
2. Show examples
请等一下。
Qǐng děng yīxià.
Sandhi:Qǐng děng yíxià.
Please wait a moment.
等一下 = wait a bit
我看一下你的手表。
Wǒ kàn yīxià nǐ de shǒubiǎo.
Sandhi:Wǒ kàn yíxià nǐ de shǒubiǎo.
Let me take a look at your watch.
看一下 = take a look
我们在家休息一下。
Wǒmen zài jiā xiūxi yīxià.
Sandhi:Wǒmen zài jiā xiūxi yíxià.
Let's rest a while at home.
休息一下 = rest a bit
3. Share a tip
一下 always comes right after the verb, and it softens a request - 等一下 is gentler than 等.