Zagreb being a transit hub sees direct flights to multiple destinations including, but not limited to Dubrovnik, London, Brussels, Naples, Paris, Vienna, Dusseldorf and Zurich. The airport is located approximately 45 mins away from the town centre and airport shutle buses and cab are easily available from outside the airport.
There are a number of international bus services running to and from Zagreb to the major cities in Croatia and elsewhere. The buses are run by Croatia Bus mostly. Zagreb bus terminal website is a good medium to direct all your bus queries.