By Public Transport
The public transport network in Berlin is one of the largest in Europe. The system works on an honor system, and there are no gates where you must enter your ticket to gain access to a station. However, you must still validate your ticket in the stamping machines located on the platform or in the station. If you are caught without a valid (or validated ticket) by the ticket inspectors, you will have to pay a 40 euro fine.
All public transport can be used with the same ticket, and the tariff system is not too complex. There are three zones, A, B and C, although for most sights you will not venture out of zones A and B.
A short trip costs €1.30, and is valid for 3 U-Bahn or S-Bahn stops, or 6 Tram or Bus stops with no changes. A single trip within zones A and B costs €2.10, and allows you to travel in one direction with unlimited changes for up to 2 hours.
The best value and easiest option is usually a "Tageskarte", or day card, which allows you unlimited travel within the purchased zones for a whole day. For zones A and B, this costs €6.10.
There are also a number of tourist cards that can be bought, which offer a number of days unlimited travel on the public transport network as well as discounts into many Berlin attractions. See the Berlin Tourist Cards article for more information.
Berlin is a flat city which makes it easy to see on a bicycle. Almost all roads have a separate bike path next to them, so there is no need to dodge traffic while riding around the city. Make sure to only ride in the direction of traffic on the bike lanes to avoid a possible fine.
The center of Berlin is normally full with heavy traffic, and getting around by car is almost always a bad idea.