"Harvard is an important American university."
Translation:هارْفارْد جامِعة أَمْريكِيّة مُهِمّة.
Sentences in Arabic can be quite flexible in fact and the subject and object or predicative can be interchangeable sometimes. However, this is more into "literature" and eloquent speech.
Going back to the basics, if we are translating from English into Arabic: Whatever comes before (is) is the subject and comes first in Arabic as well. Whatever after (is) is the predicative. Second step is to check the adjectives. Adjectives come after the noun in Arabic. If there are multiple adjectives, then reverse the order. In other words, where in English the adjective that is most relevant to the noun comes just before the noun that it describes, in Arabic that adjective comes right after the noun right away before other adjectives.