Learn Russian: Надо спать.

In Russian, надо (it is necessary / must) is an impersonal word. When used alone with an infinitive like спать (to sleep), it makes a general statement meaning 'one must' or 'it is time to'. If you want to say 'I must sleep', you would add the 'to me' pronoun мне at the start: Мне надо спать.

Does надо change endings depending on who is sleeping?

No, надо never changes its form. Unlike normal verbs (such as хотеть, which changes to хочу, хочет, etc.), надо is a special unchangeable word. You just use надо plus the infinitive of the action verb, no matter who needs to do the action.

How is using надо different from using verbs like мочь or хотеть from this lesson?

While it acts a bit like a modal verb because it is followed by the infinitive спать, надо isn't actually a verb. This means you do not use standard subjects like я (I) or ты (you) with it. Instead of 'I want to sleep' (Я хочу спать), you say 'To me it is necessary to sleep' (Мне надо спать).

Can I use нужно instead of надо in this sentence?

Yes! Нужно and надо both mean 'need to' or 'must' and are almost completely interchangeable when followed by an infinitive. Saying Нужно спать means exactly the same thing as Надо спать.