Public transport (BVG) in Berlin is very good.
A map of the metro and S-Bahn stations can be found here.
Besides google maps, to find the way between two locations, a very useful app from BVG is: fahrinfo-app.
The metro and S-Bahn stations closest to the meeting place (Berlin-Brandenburgische Akademie der Wissenschaften) are:
U2 Hausvogteiplatz (240 m walk)
U6 Stadtmitte (350 m walk)
U5/U6 Unter den Linden
S+U Brandenburger Tor
Ticket machines can be found in all metro and S-Bahn stations.
Within the city centre, an AB ticket is sufficient.
To come from/go to the Berlin-Brandenburg airport (the only airport in Berlin), you need an ABC ticket.
Ticket machines at the airport are outside the airport building in case you take a bus (e.g. to U7 station Rudow) or in the S-Bahn/train station of the airport.
You can use also trains (FEX or RB14 or RE7) to reach e.g. Berlin main station or other stations (like S+U Alexanderplatz).