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 Omis.
There are local boats that run several times a day from Islands of Brac, Hvar, Korcula and Vis. Take them to Split and then use the bus or taxi service to get to Omis.
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 Omis is relatively small city.