Rail: Light rail service exists between Aksaray and Atatürk International Airport. The line goes through some major parts of the European side of the city; including the intercity bus terminal. The LRT takes the passengers to Aksaray in 30-35 minutes. The approximate cost is ?0.75 one-way. It is very easy to reach the Sultanahmet area (centre of historic Istanbul) by public transport (combination of Metro and Tram) and it should not cost you more than 3 YTL. Exit the airport and follow the metro signs to the Havalimai (Airport) metro station. Buy the tokens (tickets) and board a train going towards Aksaray. Get out at Zeytinburnu, the 6th stop and look for the tram platform on the opposite side. Board the tram going towards Eminonu and/or Kabatas and get down at Sultanahmet (16th stop) or any other stop as per your requirement. The approximate time taken for both the legs of the journey is 1 hour.
Airport Shuttle: The shuttle services are operated by Havas, which is one of the major ground handling companies within Turkey. The busses run half-hourly to Bakirköy, Yenikapi, Aksaray, Taksim Square, hourly to Kozyatagi (on the Anatolian side), two-hourly to Etiler-Akmerkez. Also, there is a fast ferry terminal in Bakirköy which connects the terminal to Bostanci and Kadiköy. Havas buses run between the airport and the fast ferry terminal according to the departures and arrivals of the ferries.
Bus: Municipality buses also run to Taksim, Etiler and Kozyatagi. This is a slower but much cheaper alternative than Havas.
Car: The airport is accessible through the coastal road, D-100 international road and TEM (Trans-European Motorway). If you are short of time or have a lot of luggage, taxi or transfer is your best option.