The biggest nearby city is Kranj.
As you leave the airport terminal, cross the parking lot and turn left. On your right you will see a road that is entering the airport zone. Walk around 150 m to the point where the road leaves from the airport area, and then you can either hitchhike there (the drivers have enough room to stop) or you can cross the road, walk a bit to the left and hitchhike there (again, enough room to stop). It is recommended to hold a "LJ" (states for Ljubljana) sign.
Otherwise, the bus ride to Ljubljana costs around 4.5 EUR.