Taking a train from Istanbul to Konya is a great way to travel when you are visiting Turkey.
There are plans for a direct train service to travel on this route, and it should be operational by 2015. This will allow for high-speed travel between the two cities.
For now, traveling by train from Istanbul to Konya is a several-step process. The easiest way is to take a bus directly from Istanbul to Arifiye and take a train to Konya from there.
Alternatively, you can take a ferry from Istanbul to Harem, then a bus from Harem to Arifiye. There you can change to a train from Arifiye to Konya.
Ferries depart Istanbul Sirkeci for Harem every 10 minutes. The Harem bus station is right next to the ferry terminal. Buses to Arifiye depart up to two times an hour and the journey takes 1.5 hours.
When you get to Arifiye, you can take a train to Konya.