fasr train from positano to venice

Positano has no rail service. Sorrento is not on the long-distance rail network, but has a commuter rail service to Naples. Salerno is on the main rail network, but is even farther from Positano than is Sorrento. It's up to you.

Bus from Positano to Amalfi, then bus to Salerno.
FR 9548 Salerno (1512) to Rome (1710)
FA 9444 Rome (1725) to Venice SL (2044)
Total from Salerno - 5hrs 32mins

There are earlier bus/train options if you want to arrive in Venezia earlier in the day, or fly there from the Napoli airport, but you won't save much time flying.

pamela,

As the others have mentioned, your only transportation options from Positano are Bus, Taxi or boat. Here are some options....

• Bus to Sorrento, Circumvesuviana to Naples and then high speed train to Venice (either Trenitalia or Italo). This is the cheapest option, especially with advance purchase discounted tickets on the fast train.
• Private car service from Positano to Napoli Centrale and then high speed train to Venice.

Travel time from Napoli Centrale to Venezia Santa Lucia is 5H:35M, with one change in Rome (that's via Trenitalia, I didn't check Italo but it will be about the same).

Thank you everyone for your help. After reading everyone's recommendations, we decided to stay in Florence and take a day trip to Venice instead of spending a day of travel from Positano to Venice.