The five deep access arches that decorate the lower part of the façade are separated by groups of columns and are all decorated with marble slabs, reliefs, fretwork, and mosaics from different ages: do not neglect them. Even the bronze doors are ancient. You can also enter from the left side, from Leoni Square, going through the so-called Porta dei Fiori, or Flower Gate, so named because it is decorated with a delicate Romanesque bas-relief of the Nativity scene.
If you prefer the colossal central entrance, which is always used by crowds of hasty tourists, don't imitate them: stop to admire the extraordinary carved Romanesque portal from the 1200s, with its lively depictions of the months of the year and various activities and crafts.
Going into the cathedral, or rather the vast lobby that precedes its true interior, you'll feel like you're crossing into the threshold of another universe. The atrium completely wraps around the front and left sides of the cathedral, while on the opposite side the empty space has been transformed into the Baptistery. The light, noises, and pigeons of the square disappear and you're welcomed into a magical, blazing space full of Venetian-Byzantine mosaics made between 1100 and 1300. You'll also immediately notice the splendor of the flooring, which is a delicate and vibrant combination of colored marble: be careful of the uneven surface caused by the yielding Venetian subsoil.
Now look up, into the golden light of the mosaics. If you have rightly decided to devote an appropriate amount of time to the cathedral, then don't go in yet, but walk along the lobby admiring the 13th-century decoration of the domes, arches, walls covered with golden-background mosaics of the sixteenth century... these are not just "any" mosaic: they are based on original designs by great painters such as Titian, Lorenzo Lotto, and Tintoretto. And don't forget the slabs with reliefs, the capitals, the medieval sculptures...
If instead you don't have much time, I recommend at least going to see the cupola from the beginning of the 13th century, located to the right of the central entrance. This cupola lets you follow the poetic story of the Genesis told in images with a bright gold background, from the creation of heaven and earth to the expulsion of Adam and Eve from Earth's Paradise.
FUN FACT: look for the last figure on the left in the portal's bas-reliefs, recognizable for his two crutches: this is the "proto", the architect of the cathedral, who's biting his hand because he was fired thanks to his pride. In fact, he had boasted of being able to build an even more splendid church than Saint Mark's!