Berlin has two international airports - Berlin Tegel and Berlin Schönefeld. Tegel is a hub airport for a number of airlines and more international airlines fly from here. Schönefeld is used more by budget airlines from inside Europe.
It is easy to reach the city center from Berlin Schönefeld, as it is connected to the city's S-Bahn network. You can catch either the S9, which takes you right through the city center, or the S45 to Hermannstrasse. You must buy a ticket for all A, B and C zones if you wish to travel to the center of Berlin, and make sure to validate your ticket before boarding. It is often not a bad idea to buy a daily ticket from the airport, as it doesn't cost too much more than a single and allows you to use the entire network on your arrival day.
Berlin Tegel is not connected to the city by train, so the only public transport option is the bus (X9 to Zoologischer Garten, or TXL to Berlin Hauptbahnhof).
A taxi to the city center would cost around €25 from Tegel, or about €45 from Schönefeld.
Berlin has high speed connections to a number of German cities, as well as to other European capitals like Vienna, Paris and Amsterdam.
When taking the train to Berlin, it is likely that you will arrive at one of three stations - Berlin Hauptbahnhof (main train station), Berlin Ostbahnhof (east train station) or Südkreuz. All of these stations are on the local Berlin transport network, so travelling to your final destination from any of these points is easy and quick.
The A9 Autobahn joins Berlin to the south of Germany, A2 to Hannover and the A24 to Hamburg. There is a ring road around Berlin, called the A10. Be aware that if you want to enter inside this ring road, then your car is required to have an emissions sticker which must be organized in advance. If you have rented a car within Germany, it is likely to already have this sticker.