1. Depending on your initial ticketing you should be able to check your bags through to SFO from FCO but you will have to collect your checked bags after clearing immigration in T1 to proceed through customs.
2. After clearing customs there is a Delta bag drop where you can drop your checked bag if tagged through to SFO.
3. Exit security and look for the AirTrain signs. Proceed to the AirTrain and take either a Howard Beach or Jamaica bound AirTrain to Terminal 4.
4. Exit the AirTrain and head to the Departures level. You can either use the kiosk to obtain your boarding pass (Alitalia may even provide you with your JFK-FCO boarding pass). You don't need your e-ticket printout but you will need your e-ticket number to enter it in at the kiosk.
5. You will have to reclear security. There is a SkyPriority line but access to that will depend on your class of travel or your SkyTeam status.