If you want to appreciate the square in all its splendor, go to the cathedral's façade near the three stands for banners (and stop to admire the beautiful bronze bases from the early sixteenth century) and turn around. From here the square looks like a theatrical backdrop enclosed between compact buildings of equal height that are perfectly harmonized, although in reality, if you observe them more carefully you'll see that they come from different ages.
To your right, the north side in the direction of the Mercerie is closed by a 150-meter long building and ends at the clock tower, which I'll discuss in a separate file. The building dates back to the beginning of the 1500s, and today houses offices and shops including the historic showroom of Olivetti, a design jewel. It's called "Procuratie Vecchie" because it once housed the residences of the "procurators", or those who were responsible for the construction and maintenance of St. Mark's, along with their families.
On the other side, on your left, you have the symmetrical structure of the Procuratie Nuove, which were built at the end of the 1500s as an ideal extension of the nearby Marciana Library. The three rows of arcades are like the practical construction of an architectural treatise inspired by classical antiquity: you can see Doric style on the ground floor, Ionic style on the first floor, and Corinthian style on the second floor.
If you look at them carefully, you'll notice that the Procuratie are not entirely parallel, but narrow down at the end. The short side, which was built in a Neoclassical style in the early 1800s, is called the Procuratie Nuovissime or Napoleonic Wing.
You should absolutely have a snack at one of the two historic venues on both sides of the square, including the most famous and exclusive Caffè Florian, which was founded at the beginning of the 1700s under the Procuratie Nuove. Its illustrious guests include the adventurer Giacomo Casanova, and great writers such as Goldoni, Byron, Goethe, and Foscolo.
FUN FACT: Caffè Florian, which together with the Procope in Paris, is the most ancient caffè in the world, was originally called "Alla Venezia Trionfante". But since the first owner was named Floriano Francesconi, all the Venetians would say, "let's go to Florian's". And so by popular acclaim, it changed names.