Learn Farsi: این نامه را زود بفرست.

It comes from the verb فرستادن (ferestādan, to send). To make a singular command (telling one person to do something), we take the present stem, which is فرست (ferest), and add the prefix بـ (be-). Notice there is no personal ending; the bare stem plus the prefix is all you need for a singular command!

Why do we need the word را (rā) in this sentence?

را marks the specific direct object of the sentence, which is the thing receiving the action. Because you are saying "send this letter" (این نامه), the letter is a specific item, so we must follow it with را. If you just said "send a letter" in general, you wouldn't use it.

Doesn't زود (zud) usually mean "early"? Why is it translated as "quickly"?

Yes, زود means "early," but in everyday Farsi it is also the standard word for "quickly," "fast," or "soon." When used with an imperative (command) like this, it simply means you want the action done right away.

Why does the verb بفرست (befrest) come at the very end of the sentence?

Farsi sentences typically follow a Subject-Object-Verb order, meaning verbs almost always go at the very end. Even in commands where the subject "you" is implied and left out, the verb stays at the end, coming after the object (این نامه را) and the adverb (زود).