Istanbul has a great public transportaion system that consists of buses, trains, trams, a subway, and ferries. If you are going to be in Istanbul for two weeks or more, I suggest buying an Akbil. An Akbil is a multipurpose pass that you buy for 6 million TL from any "Akbil Satýþ Noktasý" in the main bus terminals (i.e. Taksim, Beþiktaþ, or Eminönü). You can then add as much money as you want. The Akbil can be used on all public transportation, which is what makes it so useful. Each time you use the Akbil, money will be deducted. When you run out, you can just refill. There is a student fare so when you buy, show them a student card.
The most exstensive and convenient form of transport are the buses. You can get to any part of the city by bus. Buses cost 500,000 TL for students and the elderly, and 750,000 TL for everyone else. Tickets, or an Akbil, are needed to ride the bus. Tickets can be bought from the white ticket sales booths at major bus stops, or on some buses. There are two types of buses: the blue buses (which you can buy a ticket on) and the green or orange buses (for which you must have a pre-bought ticket to ride). Buses run circular loops and the route is posted on the side of the bus. The sign will have the starting point, the end point, and then the major stops in-between. All buses are also numbered and I will always use bus numbers whenever possible in this journal.
Istanbul has a tramway that runs from Eminönü to Zeytinburunu. It is mostly for commuters, but will be useful for tourists for getting around Sultanahmet to places like the Grand Bazaar and the buses and ferries at Eminönü. You can buy tickets at any stop, or use your Akbil.
The Istanbul Metro is still under construction and only has two lines up, again mostly for commuters, and are not of much help to tourists. There is a line the runs from Levent to Taksim and one from Yenibosna to Aksaray. It is cheap and clean, but unfortunately not terribly useful yet, hopefully more lines will come.
The Istanbul ferries and Sea Buses are great ways of getting accross the Bosphorus and to places like the Princes Islands and Anadolu Kavaðý towards the Black Sea. Ferry docks are all around the city, the main ones being Sirkeci, Eminönü, Uskudar, Harem, Kadýköy and Beþiktaþ. You can buy tickets at any dock, or use an Akbil. The fare will depend on the route, and Sea Buses, although quicker, are more expensive.
Istanbul also has a few commuter trains that will not be terribly useful to tourists.