I am traveling to Italy in June and was wondering how far in advance I should make reservations on the Eurail
You can actually buy them from Trenitalia when you are in Italy. As I said in my reply to your other post, the trains rarely sell out. They hold a lot of people and and are very frequent, like at least once per hour on the main routes like Naples to Rome to Florence to Bologna to Milan to Turin or to Venice.
You must know specifically which Freccia or Intercity train you want to take before buying the reservation, as the reservation will only be valid for that specific train. To maximize flexibility on when you want to travel, buy the reservations at a train station in Italy. This can be done on your travel day or in advance of your travel day.
Don't buy reservations for .Italo because although the trains are beautiful and fast and often cheaper than Trenitalia - leather seats too, even in the cheap seats - because .Italo does not accept Eurailpasses.