Learn Italian: Ho scoperto questo scheletro di dinosauro un mese fa. - I discovered this dinosaur skeleton a month ago.

The word fa translates to the English word ago. Just like in English, it always goes immediately after the amount of time. It actually comes from the verb fare (to make or do), so un mese fa literally means it makes a month.

Does the word fa change if the time period is plural?

No, fa stays exactly the same no matter how much time has passed. For example, two months ago is due mesi fa and many years ago is molti anni fa.

I see ho scoperto means I discovered, but what is the dictionary form of the verb?

The dictionary form is scoprire (to discover). It has an irregular past participle, which is why it does not end in the usual -ito. It follows the exact same pattern as aprire (to open), which becomes aperto.

Why is it scheletro di dinosauro instead of just dinosauro scheletro?

In English, we often stack nouns together to make terms like dinosaur skeleton or coffee cup. Italian does not do this. Instead, you use the preposition di (of) to link the two nouns, literally saying skeleton of dinosaur.