There are two main docks from which you can take ferries to Costiera Amalfitana, Capri and even Ischia. There are Molo Manfredi and the other one is Piazza della Concordia.
For example one way trip from Salerno(Piazza della Concordia) to Amalfi takes around 35 minutes and one way ticket costs 6 euros
More than Salerno the best to view there is the Amalfi Coast. So you can take a boat in Salerno harbour (not far by walk from train station about 1Km) and then go towards Positano, Amalfi, Furore Fiord, etc...
There are SITA buses along the coast with one end at Salerno. So, one can easily reach Positano and Sorrento with a change at Amalfi. It is absolutely one of the most spectacular bus rides in the world. Local buses also reach Pompeii and Pastrum.
Air: the closest airport is in Napoli. It will take you one hour to drive from there to Salerno and two hours from the airport to Amalfi.
Train: easy train connections until Salerno or Cava dei Tirreni (if you want to go to the Costiera Amalfiitana), along the Roma-Napoli-Reggio Calabria line, then you have to go by bus.
Car: take care of the road. The Costiera Amalfitana is famous because there's never a 100-metre straight line, the road is very very narrow and it goes right on the border, maybe 100 metres above the sea. with the cliff on your internal side. As you may imagine, 'locals' drive fast because they suppose they know the way, they're always bored to have to drive slowly and they always hope no one else is driving the opposit direction.
From UK Fly with Alitalia with one change over in Milan or Rome on both out bound and inbound journies.
Direct flights are from London Gatwich with British Airways. Flight time 2.15 mins.
All major european air lines fly via their operating hub
Bus -Orange bus for all the local trips Blue bus (SITA operator) for you long distance trips.
Buy bus and foot