The easiest and the cheapest way is to book your transfer directly to Novi Sad EXIT here.
By Taxi: If you decide to take the taxi from the Belgrade airport to Novi Sad, the ride will cost you between 50 and 80 Euros (per cab, not per person). You shouldn't have to pay more and make sure to find out the price beforehand. The trip will take you about an hour.
By Bus: There are NO public bus services from the airport to Novi Sad, you need to get a bus to Belgrade centre, and change onto a bus or train to Novi Sad. See 'By Bus' section.
Belgrade Airport to Belgrade Bus/Train Station:
Belgrade airport is 15km from the centre of Belgrade. One bus stop is next to Terminal 1 and the other one is in the front of the Arrivals entrance.