Tickets
A standard ticket is valid on all the different types of transportation with unlimited changes.
Berlin uses a zone system, but you are unlikely to need to go beyond zone A & B, except on trips to Potsdam. This is a very large area, even including Schönefeld airport.
If you're going to be traveling a lot by public transport, consider getting
a Tageskarte day card - €6.10 for zone A & B
or
the Berlin WelcomeCard, which gets you unlimited travel
in zones A and B for €16/21 for 2/3 days, or
in zones ABC for €17,50/24 plus discounts at many of Berlin's tourist attractions.
You may check if you want to visit some of them, cause otherwise it's not profitable, as it's more expensive than 2 or 3 single day tickets.
Weekly passes for all kind of public transport valid inside zone A and B are available for €25,40.
Most of the interesting places reported here are in the A zone, some in the B zone and only Potsdam is in the C zone.
There are vending machines selling all ticket types on the platforms at every station of the U-Bahn and S-Bahn.
They offer instructions in many languages including English.
If you need assistance most larger stations have staffed ticket counters where you can ask questions and buy tickets.
Before you get on the train you need to validate your ticket using the machines on the platform or in the bus.
The machines are yellow/white in the U-Bahn and the bus, and red on S-Bahn platforms.
Validation simply means the machine prints a time stamp onto the ticket. Once validated, a ticket which is still valid will not have to be re-validated before each single trip. You will pay a €40 fine if you are caught with an unvalidated ticket.