Once you have landed and head for "Connections/transfer", there are big TK transfer/ticket desks just opposite the transfer security checks. You can't miss it.

If you have reached departure levels, head for TK M&S lounge or Business lounge where the desk staff at the entrance will be able to help you out.

It seems that you will miss TK1683 to FCO this afternoon and will be rebooked to TK1681 tomorrow morning. TK will provide hotel (quite far from the airport; near the old airport/Istanbul city), including transfer to/from airport.

Any other TK destination in Italy/Europe that will suit you better? Then ask to rebooked to there as this is invol. rebooking due to delay.