I get around, around Berlin by way of the super handy public transportation system. For a modest 79.50 euro a month, unlimited transit options can, too, be yours. Ticket prices vary depending on the zones you are traveling in- A, B, C. An A/B ticket is the most common, as it covers the entire center of the city, zone C taking up only the outskirts. If you're flying into/out of Schönefeld or want to visit Potsdam, you're gonna want a C ticket.
The S-Bahn is the second option that will be used most frequently.
With 13 lines running through the city, there's usually a train coming every 3-5 minutes. The Ringbahn is especially convenient for those who get turned around easily, as it circles the city (hence the name) and can easily get you to a connection to the line you meant to find, but got on a train going the wrong direction.
Buses are the unsung heroes of a transit system. Berlin's buses have three doors- one at the driver if you need to pay fare, two at the rear with one leading directly to the upper deck. I quite enjoy hopping on one at the beginning of a route and riding to the other end, getting a very cheap overview of the city. No tour guide to point out sites, but a greater opportunity to find interesting stuff off the beaten path.
I'm kicking myself for not getting a picture of the Tram system. I used the M10 and M8 quite frequently in my stay and they are very convenient for short distances. With over 20 lines, there's sure to be one nearby to get you to your destination or connect you to a U or S line.
Biking is also quite popular in the city, though I haven't gotten a chance to try it out. Car drivers tend to be very observant and it is expected that they will yield to pedestrian and bike traffic. Though it is also expected that everyone will respect the transit signals. You don't see a lot of crossing against a red, though the light cycles tend to be quite short, so it's not really a burden to wait.