The city with world-famous thermal springs is located 47 km from Naples, which takes approximately two hours by car. You could take a taxi, but to experience the true spirit of Italy, it's better to travel by sea.
First, from the airport, you can take a bus to the port in Naples. The ticket for the ALIBUS da Aeroporto di Capodichino al Porto (Piazza Municipio) bus will cost 3 EUR (if purchased from the driver, it's 4 EUR), and the travel time is about half an hour. You can find the bus schedule here. Then, you can take a ferry or a high-speed boat to Forte dei Marmi. The price depends on the type of transport you choose (ferry, high-speed boat, or speedboat). On average, two tickets to Forte dei Marmi with luggage will cost around 20 EUR to 50 EUR.