Learn Italian: Ho comprato questo libro l'altro ieri. - I bought this book the day before yesterday.

The spoken past tense in Italian, called the passato prossimo, works a lot like the English "I have bought." It uses a helper verb, which here is ho (I have), and a past participle, comprato (bought). You will use this two-word pattern for almost all past tense actions in everyday conversation.

Does the ending of comprato change if a woman says this sentence?

No, it stays exactly the same! When you build the past tense using a form of avere (to have) as your helper verb, the past participle (comprato) always ends in -o, regardless of whether the speaker is male or female.

What is the literal translation of l'altro ieri?

It literally means "the other yesterday." L' is "the" (shortened because altro starts with a vowel), altro is "other," and ieri is "yesterday." This is the standard Italian phrase for "the day before yesterday."

Why don't we need to say questo il libro for "this book"?

Questo means "this" and acts as a pointer that takes the place of words like "the" (il). Just like in English, you wouldn't say "this the book," so in Italian you just put questo directly in front of the noun libro.