Translation:I had found out about it from the newspaper.
Because the lesson is about past imperfect, which implies that you have to build your sentence using had + past participle, even though preterit alone would often do it in spoken English. But there is actually the same difference in meaning in German and English between a past action (preterit) and another prior to that (or any past) action. Of course this would all be much clearer in context.
As a native English speaker, this sentence sounds to me like you found out about something next to the newspaper. Using "by" like this evokes its locational meaning. "By way of" is regionally correct; I rarely would use that phrase, though. I would just say "in the newspaper". The information is "in" the book/paper/magazine/box/house.
"Ich hatte durch die Zeitung davon erfahren." 1. Why is "davon" last before the infinitive? Is it treated here as an accusative noun? Otherwise I'd expect it to be before "durch die Zeitung." 2. I actually used "Ich hatte es . . .", which was accepted. What is the difference in meaning or preference between using "es" and "davon"?