Travelling in Istanbul using public transport is easy, reasonably priced and safe. I have had the pleasure on two occasions to undertake research in this interesting city. Other colleagues have also had that opportunity and you can read one of their experiences here.
This particular station is Gulhane on route T1 and the service is heading in the direction of Kabatas.
A section of the most recent map licensed by Communicarta to National Geographic Society and available in their Walking Cities guidebook. This map features all the different transport types a visitor will need to get around easily, including the ferries (three of them can be seen here in red, green and orange, lines 2, 3 and H)
There has been a lot of work undertaken over the years in Istanbul to improve public transport and there are now many more parts of the city easily accessible, including being able to travel by rail from Europe to Asia.