The easiest and most flexible way to reach from Berlin… from mainland Europe. Mind you: inside the S-Bahnring (basically the entire huge city center) you need an environmental permit. You can get one at specific fuel stations in the country, or request one in advance. If you don’t have a permit, the easiest thing is to park your car at a huge station along the S-Bahnring and then take public transport. A good and typically German alternative can be the Mitfahrzentrale (ride-sharing service), for a small compensation you drive to or from Berlin with someone who coincidentally has to travel the same stretch.
There are several cheaper options. EasyJet and Ryanair all fly to Schönefeld airport, the bigger companies fly to Tegel airport. Schönefeld lies adjacent to the new Berlin Brandenburg International, which still has to be opened after years of delay. From Schönefeld take the Regionalexpress (every fifteen minutes) to Hauptbahnhof (30 minutes) or the S9 or S45 (every 10 minutes). Mind you Schönefeld and BBI are in the outer zone (zone C) of the public transport system, you need an ABC ticket to get into the centre. From Tegel you can take buses TXL (Hauptbahnhof and Alexanderplatz) or 128 (switch to U6 at Kurt Schumacher Platz or U8 at Osloer Strasse).
Not faster, but more comfortable can be the trip by train. No security checks on airports and no luggage limitations.
Don’t try to save money here, buy a day ticket (or a week card) for public transport. That’s the best, safest and cheapest option. Tickets are valid for bus, tram, U- and S-Bahn and regional trains inside Berlin. A ticket for the AB-zones usually does the trick, unless you want to go to Potsdam, Sachsenhausen or Schönefeld airport, which are all in zone C.
Day tickets are valid until 4AM the next day. Keep that in mind when you go clubbing, because you usually don’t go home before that time. And you don’t want to get caught during one of the many flying checks by people in civilian clothes: you will only recognize them when they, immediately after leaving a station, identify themselves and ask everyone to show their tickets.
There are also Citytourcards and Welcomecards, especially for tourists. With that you also get discount on a variety of museums. Do your homework before you leave, to see whether such a card pays off or not.