You can see the map
Point A is the place where the bus no 72 will arrive, coming from direction of "Brankov most" (Branko's bridge), which you can see on the map. Point B is the Central bus station (departures only). As you can notice, this is not the shortest way, but, google doesn't want to show the best and mostly used one. But, I will give you detailed instructions, as I promised
Here it is!
From the point A, you should go to the south. On your left side you will see the big farmers' market "Zeleni venac". After 150m, at the first corner, you should turn right to Kamenicka ("Каменичка") street, go downstairs to the park ("Парк Луке Ћеловића" on the map), pass through the park, cross the street once, and then one more time to the left and you are in front of the bus station. Don't be confused if you see the buses in "Park Bristol", that is only arrival station.
Another option, much easier for you, is if you use the bus A1. It will stop in front of the Railway station, you can see it at the bottom of the map, 200m southeast from the Central bus station. You can't miss it
Bus no 72 is a public bus, which has a lot of stops on its way, but the one where you will go out is the last one. The ride takes around 40min. After you cross the bridge, pay attention when all the people go out
You should buy the ticket inside the bus, or better at some shop inside the airport. The ticket should cost around 80 dinars (0,80 EUR). Inside the bus it is more expensive. It is necessary to validate the ticket in the machine inside the bus!
Bus A1 is better and easier option for you. The ticket costs 250 dinars (2,5 EUR), and I think you can buy it inside the bus. It has only one stop before the Railway station. It will cross another bridge, the one where is written ("Земунски пут"), pass by the Central bus station and stop in front of the Railway station, which is 200-300m far. You can see the schedule and the map here:http://www.beg.aero/upload/Mapa_i_tabela.pdf
Red line is the direction to
the airport, and the brown one from
the airport. The stop with the name "Желез. станица" is Railway station.
You can't get lost now
Good luck and welcome!
PS: The name of the airport is "Nikola TeSL
a"! It got the name by our, definitely most famous, scientist and one of the most important scientists in the human history http://en.wikipedia.org/wiki/Nikola_Tesla