Learn Russian: Он работал сутки. - He worked for twenty-four hours.

Сутки means a full 24-hour period (a day and a night). We use день when we just mean the daytime or a general day, but сутки is specifically used when talking about a 24-hour shift or a full 24-hour cycle.

Why isn't there a word for "for" in the Russian sentence?

In Russian, when you want to say you did something "for" a certain amount of time, you don't use a preposition. You just put the time word directly into the sentence using the accusative case. For сутки, this form looks exactly the same as its dictionary form.

Is сутки a singular or plural word?

It is always plural! Just like "scissors" or "pants" in English, сутки has no singular form in Russian. Even if you are talking about just one 24-hour period, the word behaves as a plural noun.

Why is the verb работал imperfective here?

Because the sentence focuses on how long the action lasted (a full 24 hours). In Russian, when you state the duration of an action using time expressions, you almost always use the imperfective past tense, like работал.