The border between the Vatican and Italy is ambiguous. The Vatican is an enclave of Italy and therefore has about a two mile long border. This border alternates between being porous and protective. In the south and west the Vatican's border follows the old Leonine Wall that was built by previous Popes for protection.
While most of the Vatican territory is enclosed by the wall there are some gaps. Most noteably, St. Peter's Square is split between Italian and Vatican territory by a white line painted on the street.
There are five entrances to the Vatican City all of which are guarded by the Swiss Guard. The most popular and easiest is through St. Peter's Square through the Villa della Conciliazione or through the Vatican Museums on the Viale Vaticano. The Vatican does have its own passport but entrance into the city does not require passport identificication.
The Vatican's borders are also vague because the Vatican engages in Extraterritoriality. The Vatican owns various buildings in Italy that while on Italian land have a status similar to an embassy. If you follow the hyperlink you can see in the lower left corner of the map that several of the Vatican's buildings are in Italian land. One of the most notable pieces of land that enjoys this status is the Papal Palace of Castel Gandolfo. Owned by the Pope, this land includes 55 hectares of land and is where the Pontifical Observatory is located.