There is no airport in Delphi. The most convenient airport to go to Delphi is the International Airport of Athens that receives flights from many airports around the world.
From Athens, you can go to Delphi by bus. There are daily buses to Arachova-Delphi that depart from Liossion Bus Station in the center of Athens. The bus trip is about 3 hours. Alternatively, you can go by rental car.