Learn Hardcore Russian: Мне нужно подумать, прежде чем ответить на сложный вопрос. - I need to think before answering a difficult question.

The word нужно is impersonal and requires an experiencer in the dative case. Literally it means “to me is necessary,” so you always say Мне нужно, not Я нужно.

What does нужно подумать mean, and why use подумать instead of думать?

нужно is a modal word expressing necessity, always followed by an infinitive.
думать is the imperfective infinitive “to think” (ongoing or habitual).
подумать is the perfective infinitive “to think (through to completion or for a bit).”
Using подумать implies you want to finish the act of thinking before moving on.

How does the construction with прежде чем work?

прежде чем means “before (doing something).” It introduces a subordinate clause or an infinitive, linking two actions in time. Here it shows that the act of thinking happens prior to the act of answering.

Why is ответить in the infinitive here instead of a finite form like я отвечу?