Empires and Barbarians: The Fall of Rome and the Birth of Europe by Peter Heather is a solid evidence based look at this. Lots of what I would call archaeology involved to anchor writings in facts.

Unfortunately we don't have a huge amount of sources on Germanic tribes who operated largely outside the Roman sphere of influence. This is due to a lack of written culture amongst the early Germanic tribes. Much of what we can surmise is based on the archaeological record, but even here there are issues - especially when historians try equating language, material remains and culture. From around 400 - 800 AD, around the fall of the Roman Empire, there were huge population shifts in the region as well, with Germanic peoples such as the Vandals and Goths displacing established populations. Earlier, around 200BC - 200AD, there was a gradual displacement of a 'Celtic' culture from Southern Germany to west of the Rhine. Thus it's hard to talk about one continuous culture east of the Rhine. As best as we can tell, there was an ever-shifting mixture of Celtic, Germanic, Slavic and Baltic-type groups.

The biggest written source on the people east of the Rhine is, as /u/danjnk mentions, Tacitus' 'Germania'. This was written c.98 AD by a Roman historian, and is an ethnographic work describes the customs of the 'Germanic' peoples. It also goes into some detail on the different tribal divisions and branches. However, we have to take Tacitus with a pinch of salt. Partly this is because all the information is second-hand, and inevitably corrupted or distorted to some extent. Secondly, historians today agree that a major purpose of the work was to show the Germanic tribes as a counterpart to the Romans. Tacitus holds the Germanic people up as examples of good character in contrast to what he perceived as a weak, vice-prone modern Roman society. Given this ulterior motive, we can't take Tacitus' praise at its word. However, I would encourge you to start by finding a translated edition and to read it with a sceptical mind.

Tacitus' 'Annales' are another source, and a major source for the life of the most famous Germanic chieftain, Arminius (also known as Hermann in Germany). According to Roman sources, Arminius was a member of the Cheruscan tribe. He was sent to Rome as a hostage when young, but returned to fight against the Romans as they attempted to conquer beyond the Rhine c.7 AD. In 9AD, an alliance of Germanic tribes defeated the Roman legions in the Battle of the Teutoburg Forest. Archaeological evidence backs up the Roman accounts of this disaster and places the battle in lower Saxony. Unfortunately for the Germanic tribes, the Romans re-invaded under the Emperor Tiberius' nephew, Germanicus Julius Caesar (not to be confused with the famous Julius Caesar). From 14AD onwards the Romans inflicted severe defeats on various Germanic tribes until they decided that the price of conquering east of the Rhine was not worth it.

I'm afraid that all the secondary sources I can think of off the top of my head are in German. I found what looks like a decent introductory article on Roman-Germanic conflicts here. Definitely start with Tacitus, though - he's still the starting source for most modern historians. Perhaps someone else can recommend an archaeology-based source, since I don't know much about that field.

Tacitus's Germania?