Learn Italian: I miei cani hanno sempre fame.

Possessive adjectives must match the noun they describe in both gender and number. Since cani (dogs) is masculine plural, you need the masculine plural article i and the masculine plural possessive miei.

Why do we need the word i here? Can I just say miei cani?

In Italian, you almost always need a definite article (like il, la, i, or le) before a possessive adjective. While in English we just say "my dogs", in Italian you literally say "the my dogs" (i miei cani).

Why does the sentence use hanno (they have) instead of saying "they are"?

In Italian, you do not say you are hungry. Instead, you say you have hunger. The sentence uses the verb avere (to have) combined with the noun fame (hunger) to literally say "my dogs have always hunger".

Since there are multiple dogs, shouldn't fame be plural too?

No, because fame is a noun meaning "hunger", not an adjective describing the dogs. Just like in English you wouldn't say "they have hungers", in Italian they all experience the singular concept of hunger.

Why is sempre placed after ?