Learn Farsi: تیر ماهِ چهارم است.

Counting numbers like chahar (four) do come before the noun. However, ordinal numbers ending in -om (like fourth, fifth, sixth) act exactly like adjectives. They come after the noun they describe and are connected to it with the invisible 'e' sound called the ezafe. That is why we say mah-e chaharom.

How exactly is the word chaharom (fourth) formed?

It is very simple! You just take the regular number chahar (four) and add the suffix -om. This works for almost all numbers in Farsi to turn them into ordinals (ranking numbers), like panjom (fifth) or sheshom (sixth).

What exactly is Tir?

Tir is the fourth month of the official Iranian solar calendar. Because the Iranian new year begins on the first day of spring, Tir is the first month of summer, roughly corresponding to late June and most of July.

Would I hear native speakers say ast at the end of this sentence in everyday conversation?

Probably not. The word ast is the formal, written way to say 'is'. In casual spoken Farsi, people usually drop ast and attach the spoken 'is' sound directly to the end of the previous word. A native speaker would normally say Tir mah-e chaharom-e.