Just like every major city in the world, Berlin has a very good public transport network.
The easiest way to get around the city is by S- and U-bahn. The S-bahn are the trams above ground and the U-bahn is the underground.
But there are also busses, ferries and many taxies in Berlin.
The city is devided into 3 zones, Zones A, B & C.
Zone A is the city centre inside the “Ring-bahn”. This “Ring-bahn” are the S-bahn lines S41 (Clockwise) and S42 (Counter-clockwise).
Zone B are the cities suburbs, like Spandau but also the Olympia Stadion and airport Tegel.
Zone C are all the cities and villages close to Berlin, like Potsdam and airport Schönefeld.
You can get a free map of the network at every station, but even more easy to use is the free to download Fahrbahninfo Berlin mobile app.
You can buy tickets for all public transport at the many stations. For tourist who stay a couple of days in the city it is more easy to buy a 48hr or 72hr multi-day ticket. But you can also buy just a one-trip ticket which is usable for only 2 hours.
For more information about the Berlin public transport, the journey planner and buying tickets, go to the website of the Berliner Verkehrsbetriebe BVG.