Learn Farsi: من روزنامه‌ی قدیمی یا گران نمی‌خوانم. - I do not read an old or expensive newspaper.

یا (yâ) means "or". In this sentence, it joins the two adjectives قدیمی (old) and گران (expensive) to describe the newspaper. Just like in English, you place it directly between the two choices you are connecting.

Why does روزنامه (newspaper) have a ‌ی (-ye) attached to it?

That is the ezafe! Because روزنامه ends in a silent "h" (ـه), it takes the ‌ی (-ye) suffix to connect it to the adjective that follows it (قدیمی). This links the noun to its description.

Wait, if there are two adjectives (قدیمی and گران), why is there only one ezafe?

The ezafe is only needed to connect the noun to the first adjective. Because the two adjectives are connected by the conjunction یا (or), they act as a single descriptive phrase, so you don't need another ezafe between them.

The English translation says "an old or expensive newspaper", but I don't see the word for "a/an" (یک) in the Farsi sentence. Why?

In Farsi, when you are talking about a general habit (like what kind of newspaper you read), you often don't need to use یک (yek). A simple singular noun like روزنامه can translate to "a newspaper" or "newspapers" depending on what sounds most natural in English.