From the airport you can use public bus services:
Mini Bus line A1 (Airport-Slavija Square)
From Slavija Square (the last stop of mini bus A1) to the Downtown Central hostel you can use trolley bus 19, 21, 22 or 29- thirth stop of the trolley bus is in front of the Downtown Central hostel.
PTC Belgrade Line 72
It will take you through several parts of Belgrade before arriving at its final stop near the Zeleni Venac green market in the city center which is within walking distance of the Downtown Central Hostel.
Train and bus station are within walking distance of the Downtown Central Hostel. (1,1km)