Map shows airport location and location of city main transportation points.
Shuttle bus 101 serves airport. But in fact the last stop is located in Chornobayivka village near turn from the motorway, 3 km from airport. You can take a walk or take a taxi.
Shuttle bus 101 passes central bus station, Zaliznychna street (not far from railway station), Central marketplace (local bus station, city center).
Update, 3 Nov 2014: shuttle bus passes airport, at least during arrival and departure of Istanbul flight.
Airport located outside Chornobayivka village near E58 motorway (Odesa — Mykolayiv — Kherson — Melitopol — Novoazovsk). Visible sign is located near turn from the motorway - aviators memorial, MiG-19P aircraft on the base.
You can order taxi to get to/from the airport.
Світлофор (Svitlofor) - +380 50 3964055, +380 67 5533055, +380 552 393055, +380 552 225682
Економ (Econom) - +380 93 9015815, +380 96 8876815, +380 50 3535515, +380 552 391515
РікоТаксі (RikoTaxi) - +380 95 2776565, +380 50 3186565, +380 67 5516565, +380 552 320749
As for 3 Nov 2014 taxi trip from the city center to the airport (Svobody sq., "Svitlofor" taxi) cost 68 UAH (4-5€).
After Istanbul flight arrival, taxi drivers are waiting near exit from the terminal building. Prices could be much higher that usual tariff. You can try to bargain. E.g. they asked 100 UAH for trip to one of the city's neighborhoods, but they lowered price to 50 UAH after bargaining. Also you always can order taxi using the phones above.
From Simferopil, Crimea
Passangers can travel to Crimea and back with a shuttle bus on route Simferopil - Kherson (airport and railway station) - Simferopil. Onew way ticket costs 1500 russian rubles (approx. 25 USD).
Find contacts for transfer booking on carrier's Facebook page https://www.facebook.com/sipkhe.