There are two inexpensive ways to get from the airport to Taksim. You can take the airport shuttle bus directly to Taksim Square. Contact Cem by phone and he will come get you.
You can also take the tram from the airport to Tophane. Take the to Aksaray, where you will get off and transfer to the Kabatas tram. Get on and take the tram to Tophane, where you will get off. At Tophane. Contact Cem by phone and he will come get you.