Take a flight to the Split Airport and then use a Bus service to get to Omiš.
You can use services from frequent buses that come in and go from Split, Makarska, Sibenik, Dubrovnik, Rijeka, Mostar.
Local bus line 60 departs from Sukošanska bus terminal in Split every 30 minutes. A one-way ticket to Omiš costs 20 kuna (available in bus), while a round-trip ticket costs 31 kuna and can be bought only at kiosks.
There is taxi-van service that can be used from Split and Makarska.
There is a ferry service from Ancona, Italy. Take a ferry to the Port of Split and than use the bus to get to Omiš.
There are local boats that run several times a day from Islands of Brac, Hvar, Korčula and Vis. Take them to Split and then use the bus or taxi service to get to Omiš.
You can get around the city by car, local taxi and bus service, or tourist trolley. You can also rent a bike or moped from tourist agencies. However most people find it sufficiently comfortable to get around on foot, because Omiš is relatively small city.