The best way to arrive to your hotel from the airport, if you have not arranged a shuttle transfer, is to take a taxi. Do not negotiate the price but use the taxi meter all the time (which is the legal way), this is for your adventage.
Istanbul have %125 more traffic than the normal (which is %50) during the rush hours. So it may take up to 1 hour to downtown, and also about 60 Turkish Liras. Normal case it is about 50 Turkish Liras.
Always take a taxi from the station or call it from the hotel. If you forget something in the car you always have a chance to contact the driver this way.
Welcome to Istanbul :)