Spandau is the terminal station for a couple of public transport lines especially the backbone line U7 and several regional trains stop frequently when they cross Berlin and Brandenburg.
By plane
Airport Tegel is located in the southwest of Reinickendorf, 15 minutes distance from the center of Tegel. From the airport you can get into the center of Berlin with the bus lines TXL, 109 and X9 or into the center of Tegel by bus 128 change at Kurt-Schumacher Platz to U6 to Alt-Tegel. From the center of Berlin take the U-Bahn line 6 to Alt-Tegel, or the S-Bahn line 25 to station Tegel if you want to get into the center of Tegel.
By public transport
The main backbone for Spandau the western parts is the U-Bahn line U7 with the major stations Zitadelle, Altstadt Spandau and Rathaus Spandau. The S-Bahn lines S5 end/starts here as well.
The BVG the public transport company runs a public ferry between Kladow and Wannsee which is primarily designed for commuters.
U-Bahn line 8 and S-Bahn lines 1 and 25 go through Reinickendorf; main stations are Alt-Reinickendorf S 25 and Rathaus Reinickendorf U8.
To get into Pankow, get out at S-Bahn/U-Bahn station Pankow.