You can get to Dalmatia directly by ferries from Italy - from Ancona, Bari and Pescara, as well as by Jadrolinija ferries which are sailing along Dalmatian Coast from North Adriatic's city Rijeka. Numerous local ferry lines connect Dalmatia mainland with it's islands aswell.
Dalmatia by plane
Zadar, Split, Dubrovnik and Brac island have airports that are served by airlines.
Dalmatia by bus
Various and very frequent bus services run from Zagreb Bus Station to the Dalmatian cities and towns as well as coast. Also there is a very frequent bus service along Dalmatian coast that connects Dubrovnik area with Split, Zadar and Rijeka as well as all other stops on the route.
Dalmatia by train
Train services runs from Zagreb to Split and Zadar.