You are going to Sakaiminato City.
To Yonagokuko Station
Take the train from Yonagokuko (Airport) Station to Sakaiminato Station on the JR Sakai line.
As you exit the airport building, turn right.
Continue straight; the station is less than 5 minutes away.
You will reach a staircase and elevator.
The staircase leads to an overpass, which leads to Yonagokuko Station. The elevator can also be used.