How do you get from Split to Split Airport? The web is filled with spam regarding this and the websites for the options lack timetables etc.
There are busses that depart from the main station and two companies occupy the route;
Price and route is the same so just pick the one where there's a lot of people.
There's also the Sukoišan Bus Terminal with airport connections, namely bus 37. Trogir is a town west of the airport, Split is east.
There are taxis just north of the bus station (3 meters) and you should always ask for a fixed price, e.g. 250 kn. Else it can get much more expensive. You might have to ask around to get a fixed/good price but that's no problem, there's no "taxi queue" there that you might find at other places.