Despite some minor glitches in the past, public transport works reasonably well in Berlin. All major airports (TXL and SFX) are connected to the local public transport systems. Tickets are available as whole-day tickes for little more than six Euros, tickets that are valid for two hours (well sufficient to commute between most places in town) are available for little more than two Euros. Information on iternaries and on the network are available at https://www.bvg.de - there is a button to switch to English at the top of the page.
If you prefer to go by cab - they are available at every major airport and train station as well.
Renting a car is possible as well. Berlin is really easy - if you are used to local traffic. People do watch out for each other, parking is free in most areas (except for tourist areas of course).
If you want to spend a day for sight seeing, consider renting a bike at one of the local shops to get around. Distances usually are too large for walking.