You can come to Zagreb using 4 modes of transportation. It's 5 if you use a bicycle, but that really isn't so popular.

1. By plane

You'll probably arrive at Zagreb Pleso Airport. If you plan to arrive at Ljubljana Airport, which is about 100 mi away from Zagreb, you should plan on how to come to Zagreb in advance (there are numerous buses and trains from the city of Ljubljana (not LJU airport) to Zagreb, for example). So, if you arrive/depart to/from ZAG, there are three options of transportation to the center of the city:

a) bus which goes from the airport to the bus station in the center of Zagreb - it costs about 4€ (prices change, though, and it might be payable only in kunas). It departs (with some exceptions) each 30 minutes from about 6am to 9pm both from the airport and from the bus station.

b) local public transportation bus which goes from the road half a mile from the airport to the railway station - it costs about 1.5€ (only payable in kunas). This option is only recommended only experienced travellers as you have to leave the airport on foot and walk about 10 minutes until you reach a small intersection. There is a bus station. The bus comes appx. every 10 minutes during daytime.

c) taxi - unfortunately, it's probably your best bet during nighttime. It costs about 25-30€ (it might be payable only in kunas, ask before you come inside to be certain) depending on where you want to go. Count on the fact there may not be any taxes available on site, in which case you should call 970 and talk to the taxi operator. Make sure the taxi driver turns on the taximeter. That kind of scam doesn't take place often, but... better safe than sorry.

2. By bus / by train

Buses and trains come to the bus station and train station, respectively (obviously :) ). They are both right in the center of the town and public transportation is readily available both during daytime and nighttime (although night trams should never be your choice). Also, there are taxis available on site.

3. By car

If you're in a car, you have no problems. Just avoid rush hours, drinking alcohol (zero tolerance in Croatia) while driving and be sure to have a lot of patience while driving in the center (slow moving traffic at most times).