Learn German: Viele Grüße aus Italien!

In German, the standard way to send regards on a postcard or in a message is viele Grüße, which literally means "many greetings". English speakers usually say "Best wishes", but this is the natural fixed phrase in German.

Why is the preposition aus used here instead of von for "from"?

When you are talking about coming from a geographical location like a country, city, or continent, German uses aus (which literally means "out of"). You would use von if you were talking about coming from a person or a specific event.

Why is there no article before Italien? Don't some countries need them after prepositions?

Most countries in German, including Italien, are neuter and don't use an article when saying where you are from. You only add an article for the exceptions, such as feminine countries (like aus der Schweiz for "from Switzerland") or plural countries (like aus den USA for "from the USA").