There are several excursion and small boats running a long the Bosporus, However I advice you to take a regular Ferry.Istanbul
Ferries to the Bosphorus leaves from Eminonu, so take a tram and reach to Eminonu.. There are 3 ports at Eminonu and the ones running in the Bosphorus are leaving from number 3 port.. Ferries leaves at 10:35, 12:00 and 13,35 in summer.. Ticket cost is 7,5 TL (~5€) for return and 4 TL for one way. During winter season (31 Oct - 1 May) only 10:35 ferry operates.
We call the Bosphorus ferry as the Beggar Ferry, due that it stops almost in every port a long the Bosphorus waterway and Begs:) for passengers.. When you take the boat from Eminonu to Anadolu kavagi after a tour of around 1,5 hrs you will reach the fortress at the connection of Black sea.. During your tour you will see very nice houses, old buildings along the Bosphorus and you will enjoy traveling between Europe to Asia and back again.. Please care attention to the time schedule, Ferries only operates during summer season, during winter there is only one ferry leaving at around 6 pm.
When you reach the Anadolu kavagi, first thing to do is to learn the hours of return ferry, There are again three ferries returning back and choose your desired return time... Then you can climb up to the hill and reach the walls of Fortress. There you will see the Bosphorus meeting with the Black sea. A very nice panoramic view.
In Anadolu kavagi there are many nice fish restaurants you can have lunch in one of these fish restaurants and prices are relatively cheap. After touring in the small village and having eaten your lunch, now is the time to return. You can take the ferry back to Eminonu.
Do not forget to bring your camera with you with enough films on it. ,You shall have many snaps along the Bosphorus. You can also bring a book with you. It is nice to sit at the top of the fortress and read a book. Below you can find some pictures taken during the Bosporus tour.