Plane: The Zagreb Airport provides connections especially with the other countries of Europe. Many carriers transport every day tourists from all around the world to the Croatian capital. Among the companies traveling to Zagreb are, for example, Air France, Austrian Airlines, British Airways or Croatian Airlines. For more information visit http://www.zagreb-airport.hr/flights .
To get from the airport to the downtown an easier, convenient and fast option is to go by taxi. It has a rate of between 20€ and 25€.
You will pay less for transportation traveling by bus, 4€ for travelling to the city center.
Train: By train you can travel comfortably to Zagreb traveling across Croatia. There are also direct connections to Zagreb from Austria, Slovenia and Hungary. For this you can travel from the main train station in Zagreb http://www.hzpp.hr.
Bus: Other connections to Zagreb from Europe available are, for example, the bus company Eurolines. In many cases it is the cheapest way to travel long distances but maybe it is not the best, since the trip takes time and is also tiring.
Car: The transport by car can be useful especially when you have to scroll through more cities and you go with a lot of luggage. Without problem you can get to Zagreb and then travel throughout Croatia by car as there are highways practically from all over Europe.