[verb] + 一下
[verb] + 一下 + [object]
[verb] + [pronoun] + 一下
一下 after a verb makes the action brief and low-key: you do it for a moment, without fuss. It goes straight after the verb.
Most of the time 一下 is about tone more than time. A request with 一下 asks for something small, so it sounds polite rather than bossy.
A noun object follows 一下. A pronoun such as 我 or 他 goes between the verb and 一下.
For something already done, 了 goes between the verb and 一下.
Doubling the verb, as in 看看, does much the same job and has its own point.