Here's the simplest way to get to the apartments - it's not the fastest way, but it's the least confusing...
From Tegel airport:
- Follow the signs inside the airport to the buses.
- Near the bus area, there will be a BVG counter where they sell tickets. If it's closed, there's also an automatic ticket machine outside to the right of the revolving doors. Buy a one-way ticket (Einzelfahrausweis) for Berlin AB, Regeltarif.
- You have a choice of taking any of three buses, all of which come quite frequently: X9, 109 or TXL. You have to show your ticket to the bus driver as you get on, and validate it in the little clicky machine inside the bus once you're on. (For S- and U-Bahn riding, you don't have to show it to anyone, just keep it with you and show it to the patrolers if they ask to see it.)
- If you're taking the X9 or the 109, ride the bus to Zoologischer Garten. [**Note!** I haven't been there in a while but I thought they were doing construction there this year, so if you run into random construction and somehow can't continue with my directions, take the U-Bahn, which is right there. You can hop on the U2 to Alexanderplatz and continue from there.] Assuming the S-bahn is functioning normally, take any S-Bahn going East from Zoologischer Garten station ("Richtung Alexanderplatz"). This is a pretty ride and will take you right past the Reichstag and Museum Island. Get off the S-Bahn at Jannowitzbruecke, which is one stop past Alexanderplatz. Switch to the U8 (downstairs), getting on the train going towards Hermannstrasse. You are only going one stop - get off at the next one, Heinrich-Heine-Strasse.
-If you're taking the TXL, ride it to Alexanderplatz. Then board the U8 towards Hermannstrasse. (The U8 is downstairs in the maze of tunnels - follow the signs and you'll find it!) Get off at Heinrich-Heine-Strasse.
-Once you're at Heinrich-Heine-Strasse, follow the map below to get to the apartments. You'll need step of the U-Bahn, turn left, and walk to the Northerly end of the subway platform. Climb the stairs, and you’ll be at the intersection of Heinrich-Heine-Strasse and Koepenickerstrasse. Turn right (East/South-East) and walk on Koepenickerstrasse (for two very long block lengths...past Michaelkirchstrasse), then turn right (South/South-West) right onto Adalbertstrasse (for about 1-1/4 blocks...just past Melchiorstrasse). Don't worry if the blocks seem insanely long, you are in the right place. That's Berlin for you.
-From the train station:
Depending on where you come in - Ostbahnhof, Alexanderplatz, Lehrter Stadtbahnhof or Zoologischer Garten, you'll have to adjust your plans. Luckily, all of these stations are also S-Bahn stations! So just take the S-Bahn to Jannowitzbruecke and follow the steps above that lead you from there.
... and here's a map to help you get to the apartments from the U-Bahn station.