There are 5 types of transport – train (S-Bahn) and regional train (RE); subway (U-Bahn); buses; trams or streetcars (Strassenbahnen). If you have a choice, take a train – it is usually faster! And don't be fooled by the reference to "Metro" lines: these are good, ol' buses and trams – just more frequent than the other lines!
For travel within Berlin, don't worry about zones. You have to buy an AB zone ticket anyway, covering the whole city of Berlin. If you want to travel just outside Berlin – into Zone C – then buy an ABC pass, e.g. if you visit the memorial at Sachsenhausen or go to Potsdam.
NOTE: if you are joining any Berlin Walks regular tour, you can always buy tickets from our guides or from our ticket sellers at the meeting point.
For reliable public transport information and connections we recommend using the BVG's (Berlin public transport provider) own journey planner, which you can find here: http://www.bvg.de/en (the website is in English). You can also download their app, 'BVG Fahrinfo' available on both iOS and Android. Of course, Google Maps also provides excellent information.
You can view the transport map for zone ABC by clicking here.