travel from Rome to Varenna

The name of Rome's main train station is ROMA TERMINI not terminal.
There is a regional train, called "Leonardo Express" which connects the airport station (called FIUMICINO AEROPORTO) to ROMA TERMINI every 30 min. The duration of the trip is 32 minutes. The price is €15 per person one way. No reservations on Regional trains, first come first served, just like a subway train.

From Roma Termini you will then take a Frecciarossa high speed train to Milan Centrale (~3 hr trip). Then from Milano Centrale you will change to another Regional train to Varenna (~1+ trip).. You can buy the ticket for the whole trip at the FIUMICINO Airport station if you want. The trip Roma Milan will have specific train and seat assignments, therefore you need to choose a train that departs from Roma Termini at least 15-20 minutes after the Leonardo Express arrives at Roma Termini, to allow for the train change. You could buy the Frecciarossa trip to Milan online up to four months earlier for a discounted price (called Supereconomy or Economy). Savings are substantial but discounted tickets are not changeable or refundable. Therefore if your airplane is late and you miss the train that you had pre-purchased, your money is lost. So it's a risk. If you decide to purchase a discounted ticket ahead of time, buy a Frecciarossa train that departs from Rome several hours after your plane scheduled landing, to mitigate the risk of a delayed flight.

And now a question to you.

If you intended to go to Varenna upon landing, why didn't you purchase a flight to Milan, instead of Rome? You would have saved a lot of money in train fare and flights from North America to Milan are nearly always cheaper than flying to Rome.