Learn Spanish (Latin America): Ayer publicaron un comunicado muy importante. - Yesterday they published a very important statement.

To emphasize ayer, use the verb ser in the past tense (fue) followed by the time, and then the relative adverb cuando. The emphasized sentence becomes: Fue ayer cuando publicaron un comunicado muy importante. (It was yesterday when they published...)

What if I want to emphasize the object, saying 'It was a very important statement that they published'?

You would start with fue again, add the object, and use lo que (meaning 'that which' or 'what') to introduce the rest of the sentence: Fue un comunicado muy importante lo que publicaron ayer.

Who is 'they' in publicaron if nobody was mentioned before?

In Spanish, the third-person plural (like publicaron) is often used as an impersonal form when the specific doer of the action isn't known or isn't important. It's the natural equivalent of the English passive voice 'A statement was published' or the generic 'They published...' where 'they' just means whoever is in charge.

I've seen comunicado used as a past participle (communicated). How does it work as a noun here?

Just like in English where 'a statement' comes from the verb 'to state,' Spanish frequently turns past participles into nouns. When used with an article like un, the word comunicado acts as a noun meaning 'a statement,' 'a press release,' or 'an announcement.'