Do not attempt to overtake them until the road ahead is clear; there may be more than you think and you need space to overtake them. Leave them plenty of space when overtaking; some Italian drivers give a single honk of their horn to warn of their intent. This is a non-agressive honk (simply a tap of the horn - they hold it or give several blasts if they are being agressive).
These are standard European types but differ from the UK type where there is no warning of the green signal (have that clutch engaged!). Another feature unfamiliar to northern Europeans is that "green" does not always mean total priority; if there is a signalled pedestrian crossing, they might also have a "green man" and have priority, so you must yield to them.
Pedestrian or zebra crossings
Like much of mainland Europe, the pedestrian does not have right-of-way at these crossing points. They merely indicate a recommended crossing route for pedestrians, and a likely place to encounter pedestrians from the motorist's point-of-view. In practice, some drivers will allow pedestrians cross but you cannot take that for granted. Likewise, pedestrians will cross the road at other places, even where there is a convenient crossing. As a driver you need to allow time to brake suddenly for errand pedestrians and the like.
Italian drivers give cyclists a large amount of respect, given than it is the second sport of Italy following football. You will frequently encounter them on the open road, often cycling two abreast.