The best option to visit the Amalfi coast from Naples is by bus of the SITA network. They run regularly between Naples and important places such as Sorrento, Positano, Amalfi and Ravello. Take enough time margin because during the summer it can get very busy on the road resulting in delays. In Naples there is a SITA bus station within walking distance of the cruise terminal at Nuova Marina.
TIP: If you plan to use the public transport more often consider a day ticket. Unicocampania offers several possibilities. With a combined day ticket you can make unlimited use of the various bus, metro and train companies (including Circumvesuviana) in the region around Naples. A day pass including Naples, Pompeii and all important places along the Amalfi coast costs € 12 per person. At weekends only € 6.30 per person.
TIP: A more funny way to explore the Amalfi Coast is by scooter. First, go to Sorrento by Circumvesuviana train. Walk to Corso Italia and rent a scooter for a day. You pay between € 35 and € 45 per scooter and with a full fuel tank of a couple of euros you can explore the entire coast. Just be aware of the busy and sometimes chaotic traffic.