Istanbul has 2 airports. (Ataturk airport is in the European side. Sabiha Gokcen airport is in the asian side.) From both airports you can take the shuttle bus that is called "Havatas". This is easiest and cheapest way to come to Taksim Square. Just walk downhill from the Istiklal Avenue, in 5 minutes you will see the Turnacibasi street on your right.
If you want you can ask people where the Galatasaray Hammam is since my flat is 20 meters from the hammam.