Salerno is in Campania.
Salerno is the principal town of the province with the same name, and today numbers around 145,000 inhabitants. For a brief period (February to August 1944) Salerno was the capital city of Italy, during the liberation after the allied landings before the fall of Monte Cassino to the allies and the subsequent liberation of Rome.
Today it is a lively port town, that is rapidly re-acquiring a relaxing and open Mediterranean atmosphere. The port area itself is not particularly attractive, but once you get onto the promenade things get better. Worth a visit also is the Historical Old Town, which has in recent years recovered from being a virtual no-go area to being one of the best preserved historical town centers, full of tiny little passageways and hidden corners.
Salerno was the birthplace of the "Schola Medica Salernitana" in the ninth century, which was the most important source of medical information in Europe at the time, and provided an important impulse to medical learning in Europe.
The Nearest International Airport is Capodichino (code NAP). Once you have arrived, you'll have to take one of the methods listed below to cover the final leg of the journey.
From the airport you can take a bus for 3 Euros (called Alibus) to Stazione Centrale (get off here for connections to Salerno via Train). It also stops on Piazza Municipio near the ferry port, from which you can take a 5 minute walk to catch the Bus (SITA). The route is not obvious, so see the section below.
You can buy your ticket on the Alibus, and you can get to it by walking right out of the airport terminal to the bus stop which is less than 20 metres from the airport terminal exit.
The main station is Piazza Garibaldi Station. You will have to walk a short distance to get to the station building. It's best to keep your valuables out of sight and well under supervision, as the area surrounding the train station is one of the most disreputable in all Italy. The city is trying to clear it up, but they are still quite a long way from the target.
Once you arrive at the station there are ticket machines that you can use to buy a ticket, or you can queue up for assistance at any of the ticket counters. A train ticket should cost you around 5 Euros per person.
If you can speak Italian, you can also book a ticket online, and can collect it from the ticket machine when you arrive.
By rental car
Theoretically, you can rent a car to cover the last stretch of the journey, but in all honesty it's probably better to reserve this option for second (or third) visits to the area if you are used to driving in Northern Europe of the US. The reason for this is that driving habits in this area of Italy have developed in a sort of local micro climate - most cars drift around on the motorway hovering between two or three lanes, most drivers talk and gesticulate instead of driving, and if you don't keep up with the traffic flow, you are likely to find someone tailgating you within 30 seconds or so.
If you need any more convincing, take a look at the cars when you arrive in the area. There is a prize if you can spot one without dents. Dents and rental cars don't mix well. I rest my case.
By bus from Naples
Be aware that you have to cross the road here, and that traffic in Naples follows unwritten rules that are not accessible to foreigners (or even some Italians). Red traffic lights don't always stop the traffic (the locals know the 'important' traffic lights, and will stop at these). Mopeds regularly leave the road and drive on any other surface they can find. Follow the locals, and you should be OK.
You should ask the way to the "SITA" (the name of the bus company that provides the service). If you stand where the bus stops, and face the sea (with the tall castle to your right), you will need to cross the main road and head towards the left. After about 400 meters or so, you will see a small congregation of buses to your right. Check the destination written on the bus, or you can ask for "Salerno".
The service is quite rapid for the first part of the journey, but then will leave the motorway and take a more tortuous route. The journey should take an hour so so. The ticket should cost between 3 and 4 Euros per person.
For further journeys there is a regional ticket that allows you to travel with the bus (timed limit) or train (one journey):
By bus from the Amalfi coast
You can catch a bus from the amalfi coast to Salerno, which runs along the winding roads of the coastline. The drivers are very experienced and swing effortlessly round the curves (they don't have special powers to see round corners, if you look closely, there are mirrors at strategic points). In the height of summer expect long delays, as tourist cars and buses tend to get overwhelmed by the road, and vice versa. Much better to go by boat. (See below).
By boat from the Amalfi coast