It is really easy to go to Berlin downtown from Tegel airport. You should take the bus shuffle number XX outside the airport (follow the picture of the bus inside the airport). You should buy a ticket* (<2€) for the bus in the machines close to the bus station. The bus station is only a number, don’t be scare. If you don’t speak german it is doesn’t matter, you can ask in your perfect spanglish. There is always a nice tall guy close to the machines to help you, you can also buy tickets directly to him, only be sure that the guy works for the airport…..we never know..
You should get out from the bus in XXX metro station, And look for the number XX or YY this metros go directly to downtown.
*My french credit card (carte bleue-VISA) does not work in the tickets machine in Berlin, I don’t know why. So I recommend to have euros in the pocket.