Learn Farsi: نوروز در فروردین است.

فروردین is the first month of the Iranian solar calendar. It begins exactly on the spring equinox, usually March 21st, which is why the New Year holiday نوروز happens during this month.

Do we use در (dar) for months just like we use "in" in English?

Yes! Farsi uses the preposition در to talk about events happening inside a specific month, season, or year, completely matching how we use "in" in English.

Since Farsi has no capital letters, how do I know نوروز and فروردین are proper nouns here?

Because the Farsi alphabet only has one case, you rely purely on context and vocabulary. As you learn the names of the twelve Iranian months and major holidays, you will naturally recognize them as proper nouns in a sentence.

How would a native speaker say this sentence casually?

In everyday spoken Farsi, the formal verb است (ast) is almost always shortened. A native speaker would attach it to the end of the previous word as a short "e" sound, saying "Nowruz dar Farvardin-e" instead of pronouncing the full word.