You're coming by plane
Split Airport is, following Zagreb Airport, the most important airport in Croatia. It is placed approximately 25 km west from Split, in one of the small divisions (7 of them) of Kaštel. Supported by high tech and all kinds of services that includes whole package of what city of Split offer. Local buses run 24/7 and drive you directly from Airport to the main Split promenade (Riva).
You're coming by train
Split train station is right in the center of Split. Divides you a few minutes walk from the port and from the old town and Diocletian's palace. If you see very friendly grannies to be waiting with signs "Room" saying on them at all arrivals and jumping on anyone with a backpack, you are on a right place. The train station is rather small and basic comparing with other more frequent used transportation methods.
Trains can drive customers between Split and Zagreb, Split and Perković (where you can change for Šibenik). Timetables can be found from Croatian Railways website. Trains are generally slower but slightly cheaper than buses in all of Croatia.
You're coming by ship
Ferries run 3 times a week, regardless of season, across the Adriatic to and from Ancona and Pescara (Italy). Large ferry runs twice a week back and forth the Adriatic coast from Dubrovnik and Rijeka, stopping off at a couple of checkpoint islands along the way.
Split is the main hub for local boats and hydrofoils in Central Dalmatia. Several a day run (season time) to and from Brač, Hvar, Šolta, Vis, Korčula and Lastovo. Boats are main transportation supported in city of Split because all of the islands surrounding him.
You're coming by bus
Frequent bus lines run to and from Zagreb, Dubrovnik, Šibenik, Zadar, Rijeka etc. Bus lines are frequent and relates between city of Mostar and Sarajevo Bosnia and Herzegovina), Belgrade (Serbia), Trieste (Italy) and major cities e.g. Germany and Austria. Internet pages provides you a detailed departure and arrival times.