Istanbul has a pretty good public transportation network.
The major airport, Ataturk Airport (IST) is linked to city with metro where as the secondary airport, Sabiha Gokcen Airport (SAW) is linked to city with public and shuttle buses.
The only transportation in old town is tram which runs through Sultanahmet area.
European and Asian Istanbul is connected with buses running over Bosphorus bridge, boats operating between several ports on either side and Marmaray train using underwater tunnel built in Bosphorus.
Cash is not accepted in public transport so you need to use smart tickets called Istanbul Kart. Istanbul card can be use in all ways of public transport i.e. buses, metro, tram, boats, Marmaray train. You can purchase Istanbul Kart from ticket offices at Metr stations , and kiosks available all over the city. You purchase the card empty and then you can top up as much as you want. The card can be shared, so the same card can be used by all members of your family when travelling in the city.
If you want to get your hotel in Sultanahmet from Ataturk Airport by using public transport, all you need to do is to take the metro from airport till Zeytinburnu station and there change to tram. Remember each segment of the travel will be charged seperately although it is a fixed amount.
If you want to explore Asian Istanbul, all you need to do is take tram from Sultanahmet area and get off at Eminonu, or walk to Eminonu, and then take a boat to Kadikoy or Uskudar by using your Istanbul Kart.
If you want to go to Taksim from your hotel in old town, all you need to do is take the tram towards Kabatas direction and get off at kabatas and there to change to funicular. In this travel you will be charged tram and funicular seperately.
Public transport in Istanbul runs from 06:00 till 23:30 everyday, however boats between European and Asian Istanbul starts later and finishes earlier. You need to check for all individual route.
