To take a flight from Istanbul to Ephesus, you can fly from one of Istanbul’s airport to Izmir, a coastal city near the ruins.
There are many flights a day from Istanbul to Izmir Adnan Menderes International Airport (ADB). They are operated by a number of airlines, including Atlasjet, Onur Air, Pegasus Airlines, SunExpress, and Turkish Airlines. If you take an early flight to Izmir, you can do a day trip from Istanbul to Ephesus.
From Izmir, you can take a bus or train to Selcuk, which is in walking distance of Ephesus. Buses run every 40 minutes from the airport terminals, and there are several daily trains from the airport as well. You can also book a private transfer for around 45 euros. The journey takes just over an hour.
If you don’t want to fly from Istanbul to Ephesus, another option is to take a bus. There are both daytime and overnight buses to Selcuk.