From the airport you have to get on the bus number 200 E and get off from the bus at Ferihegy Vasútállomás - Ferihegy Train Station. That is the 5th stop. You can buy bus ticket at the airport at the vending machine by bank card or cash for 350 HUF. It is also possible to purchase a ticket from the bus driver for 450 HUF only in cash. The bus driver cannot change you big banknotes. You can check the schedule here.
The Train Station is on the other side of the main road. You should cross the road on the bridge and come down at the last exit. That is the direction to Kecskemét. You can buy the train ticket to Kecskemét at the train station at the ticket-vending machine with bankcard or cash or in advance on internet. The train leaves almost every hour. You can check the timetable on the following web site: https://www.mavcsoport.hu/en
It takes about an hour to arrive to Kecskemét. Kecskemét is the 3rd stop. The price is: 1.830 HUF.
After your plane has landed, from the airport to get to Ferihegy train station, takes about 40-50 minutes.
BY TRAIN : From the Western (Nyugati) Railway Station the train leaves at almost every hour to Kecskemét. The journey to Kecskemét takes approximately 80 minutes. You can check the timetable on the following web site: https://www.mavcsoport.hu/en
The price is: 2.375 HUF.
BY BUS: From Népliget Bus Terminal (goo.gl/maps)
Check the timetable here: https://menetrendek.hu/mobile/?lng=en