Learn Italian: Prima ho mangiato la torta.

Prima is an adverb of time that can mean "first", "before", or "earlier". While adverbs of frequency like sempre (always) usually go right after the verb, time words like prima often go at the very beginning of the sentence to set the scene. You can also put it at the very end (Ho mangiato la torta prima).

If I want to say "before dinner", do I just use prima?

Not quite! By itself, prima means "first" or "earlier". When you want to say "before" followed by a specific noun (like "before dinner"), you must use prima di. For example, "before dinner" is prima di cena.

Why does the sentence use ho mangiato instead of just mangiato for "I ate"?

Italian typically uses a two-part past tense for completed actions. You need a helper verb—in this case, ho (I have)—followed by the past participle mangiato (eaten). Literally, the sentence is saying "First I have eaten the cake."

Why isn't the word io (I) used here?

Because the helper verb ho already tells us who is doing the action. It can only mean "I have", so the pronoun io is understood. In Italian, you usually drop the subject pronoun unless you want to add special emphasis.