Use S-Bahn lines 5, 7 and 75 or U-Bahn U5 to get into Lichtenberg. You can also use the regional train, but it's not as regular as the S-Bahn. The stations of biggest interests are S-Bahn station Lichtenberg where also a few long distance trains run from and Tierpark U5. S-Bahn Line 75, which goes also to Hohenschönhausen.
The S-Bahn lines 75 or 5 and the U-Bahn line 5 will get you to most parts, otherwise take the tram: the M6, for example, starts in the city center e.g. Alexanderplatz and runs through almost the entire district.
