There are two airports in Istanbul: Ataturk Airport and Sabiha Gokcen Airport.
Ataturk Airport is on the European Side. Most of the international flights arrive this airport. You can get on the airport bus to go to Taksim. To read more, follow this link, and also see the airport’s web site.
Sabiha Gokcen Airport is on the Anatolian Side. There is an airport bus to Kadikoy, and another one to Taksim. See here. There also public buses to go many places from this airport.

─ July 22, 2014