To the Belgrade Airport

The closest airport to Novi Sad is in Belgrade (70 km away), which is served by major European flight-carriers and several low-cost carriers. Daily departures and arrivals are available with European countries.

More links:
the official site of the Belgrade airport.
The national carrier Air Serbia
Traveling In Serbia By Plane (National Association of Travel Agencies).

Alternative airports: Budapest and Niš

Budapest (Hungary) and Niš (Serbia) are both about 300km away from Novi Sad, so using the airports there as final flight points can also be a good option.

Both of these cities have relatively regular trafic to Novi Sad, or transfers can be preordered in tourist offices.

To Novi Sad

When you arrive to the Belgrade airport you can easily get to Novi Sad. One of the options is to have an earlier preordered transfer from the airport to Novi Sad. It should cost about 40-60 EUR (depending on the exchange rates) in one direction and can be ordered before your arrival in many tourist offices in Novi Sad. You can also almost always ask your hosts to help you with your arrangements.

Other options are to proceed to the main coach or train station in Belgrade, and from there to Novi Sad. You can do that by airport buses (once an hour - 2 EUR) or by taxi. In the latter insist on switching on the meter - the price should be about 10 - 12 EUR. Coaches and trains go regularly from Belgrade to Novi Sad.