There are two different ways to get to Burgazada from Istanbul. You can take the ferry either in European side or an Asian side of Istanbul.

The first opinion to get to Burgazada is from European side of Istanbul. If you arrive to International Ataturk Airport, this means you come from European side of Istanbul. You can get a taxi or buses to go to the Taksim square which is the center of Istanbul, but i suggest getting a taxi because you should get on a Sea Bus from Kabatas that closer to Taksim area. If you have a taxi, you can come to Kabatas directly, if not, you have to get on to funicular metro in Taksim area in order to go to Kabatas. At Kabatas, there are some steamboats that go to the islands. Islands means 'Adalar' in Turkish. During the travel, you have to get off from steamboat at the second stop, which is called 'Burgazada'.

The second opinion to reach to Burgazada would be from Asian side of Istanbul. If you arrive to International Sabiha Gokcen Airport , this means you are coming from Asian side of Istanbul. You should get a taxi in order to arrive to the Bostanci Sea Port. At the Bostanci Sea Port, there is a sea transportation service which is named as "Mavi Marmara' , there are some also ships that are classified two categories according to islands' names. 'Heybeliada-Büyükada' and 'Kinaliada-Burgazada", therefore you should choose 'Kinaliada-Burgazada'. Sometimes, this ship rarely goes to Burgazada first but mostly it goes to Kinaliada first.