How does one get to the resort from the United States? What airports and routes are recommended?
Not got any knowledge on flights from USA but if you don't hire a car and take public transport from an international airport, there is a long distance bus stop in Rovinj and you can pick up the bus to Valalta or take a taxi from there.
Ryanair do flights around Europe to Pula and Trieste for example, so if there are no direct flights from US to those airports then you can easily find a connecting airport.
Trieste TRS in Italy about 150 km
Pula PUY in Croatia about 50 km
You will have to rent a car or organize some bus transfer from the airport.
You may also ask for pick up directly in Valalta.
Get an answer from Valalta Naturist Camp staff and past guests.