Learn Farsi: یاقوت قرمز برای پادشاه تراشیده شد.

It is made of two parts: the past participle of the main verb (تراشیده, meaning 'cut' or 'carved') and the simple past of شدن (to become). Because the ruby is an 'it' (third-person singular), we use شد. In Farsi, the passive literally translates to 'became cut'.

How exactly do I make the past participle تراشیده?

You start with the infinitive verb, which is تراشیدن (to carve, cut, or shape). Drop the final ن to get the past stem (تراشید) and just add an ه (-eh) at the end. This rule works for creating almost all regular past participles in Farsi!

Where is the word for 'the' in 'the red ruby'?

Farsi doesn't have a direct equivalent for the definite article 'the'. Whether it means 'a red ruby' or 'the red ruby' comes purely from the context. Here, we assume 'the' because it was custom-cut for the king.

How are the words for 'ruby' and 'red' connected in this sentence?

They are linked by the Ezafe. Even though it isn't written, you must pronounce an '-e' sound between them: یاقوت قرمز (yaghoot-e ghermez). This invisible vowel links a noun to its adjective.

If I wanted to say 'The ruby was cut by the jeweler', how would I add 'by the jeweler'?

In Farsi, if you know who did the action, you usually just use a normal active sentence ('The jeweler cut the ruby'). Everyday Farsi strongly prefers using the passive voice only when the doer is unknown or unimportant, so we generally don't add 'by [person]' to passive sentences.