The major work of Pliny the Elder (Gaius Plinius Secundus), which described the entire war, is lost; only once brief reference from him survives. Hence, the events have to be pieced together from the bits in other sources – and the bits of material dug out of the ground.
Four ancient historians are usually named as the chief sources on the Battle of the Teutoburg Forest (bolded part of the names are their familiar identifications):

Tacitus	Velleius Paterculus (20v.Chr.- 30n.Chr.)	Roman officer in the army in Northern Europe at the time of the German wars;
	Tacitus (55– ca. 120 AD)	a Provincial Roman from Gaul; a historian and senator during the Flavian and Adoptive Dynasties;
	Cassius Dio (164 - ca. 230 AD)	a Greek from Asia Minor; a high official the Severian Dynasty;
	Florus (unbekannt, wohl ca. 70 - ca. 135 n.Chr.)	a Provincial Roman from North Africa; a little-known author and contemporary of Tacitus.

These authors are available under the following links:

Jonas Lendering’s Dutch-based English-language website on the Battle of the Teutoburg Forest contains the English translations of the relevant sections of all four authors.
http://www.livius.org/va-vh/velleius/paterculus3.html
http://www.livius.org/te-tg/teutoburg/tacitus.html
http://www.livius.org/te-tg/teutoburg/dio.html
http://www.livius.org/te-tg/teutoburg/florus.html

That is the only English source for Florus we know of online. Good links for the other three are:
On the Bill Thayer Website:
Velleius_Paterculus: http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Velleius_Paterculus/home.html
(click to section: Book II: Chapters 94-131
Cassius Dio:
http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Cassius_Dio/home.html
(see books 55-57)
By the Project Gutenberg:
Tacitus
http://www.gutenberg.org/etext/7959
(Books 1 & 2 of the Annals, chronicled by year)

Additional Sources:

Most of the information in this section is taken from a listing of Roman sources on the Roman-Germanic Wars published in 1999 in German translation, which claims to be complete. Most of this information can also be found in English:
Krüger, Bruno, Die Schlacht im Teutoburger Wald im Jahr 9 u.Z. [The Battle in the Teutoburg Forest in 9 AD]
Beiträge zur Ur- u. Frühgeschichte Mitteleuropas, No. 18, Beier & Beran, Weißbach, 1999.
This book is in turn based on a compilation of ancient sources on all topics published by the East German Academy of Sciences in 1990:
Zentralinstitut f. Alte Geschichte u. Archäologie d. Akad. d. Wissenschaften d. DDR,
Schriften und Quellen der alten Welt, Vol. 37, 1-4, Berlin, 1990.
Krüger lists all known authors who made even cursory comments on the topic, of which there are no less than twenty-five names and several stone inscriptions, for a total of some 100 references in all. Of these, no less than sixty-four are by the above four authors, or by Gaius Suetonius Tranquillus.

On these authors:
Suetonius	tells us hardly anything about the actual fighting – and is hence often left out of the list of “major sources.” This is true both of the Battle of the Teutoburg Forest per se and of the wars before and after it; his major focus in on the domestic Roman events. He is, for instance, our major source for the reported nervous breakdown of the Princeps (“Emperor”) Augustus in reaction to the report of the catastrophe, along with the cry, “Varus, give me back my legions!” I.e., he tells us nothing about the battle, but provides a detailed account of Augustus’ reaction to it.
Florus	whom ancient historian Theodor Mommsen once dismissed as “ridiculous,” is hardly taken seriously, except by a somewhat odd “fan community” – which does, however, include one of the best known recent English-language authors on the battle, Peter Wells. He describes the legions as having gathered in a camp, where they were then massacred by a force of German who suddenly broke in – an impossible scenario. Otherwise, he reports the sinking of a legionary eagle in a swamp – although it had long been recovered elsewhere by the time he wrote that; or he recounts horror stories about what the Germans did to captured officers – which may even be true, but are not generally taken at face value, because Florus has already managed to destroy any credibility. Nevertheless, he does provide some important information about the course of the war prior to the Battle of the Teutoburg Forest.
Velleius Paterculus	is the sole contemporary witness to the events; he probably knew all the key figures personally, and provides personal information about senior officers of Varus’ army. He may also be the only source for a description of the area at Kalkriese Hill as it was during the battle – albeit a very brief description: the place where Varus’ army was finally wiped out, he says, was in the middle of “forests, swamps and ambuscades” – the latter term, “insidiae,” would if, this interpretation is correct, be the only Roman mention of the “German Wall” at Kalkriese Hill. But this interpretation, too, is controversial, and is discussed under Debates. The description of the battle is somewhat untypical for the work of Velleius, in that it is fairly factual, and Tiberius is not mentioned at all. Otherwise, this chronicler can hardly complete a sentence without heaping absolutely gushing praise over Augustus’ successor. However, his writings in that style on the fighting prior to the Battle of the Teutoburg Forest contain very useful information. He hardly describes the later years of the war at all, merely claiming that Tiberius virtually reconquered Germany in 11-12 AD. This absurd statement is nonetheless interesting, because it shows that Roman government propaganda actually covered up the defeat (see below, Tacitus). And he barely mentions the rest of the war at all, for his great hero, Tiberius, wasn’t leading the troops – his nephew Germanicus was doing that, and was defeated – and all Tiberius did was give up the war once it was clearly no longer winnable. But Velleius doesn’t go into that reasonable, but less than heroic decision.
Cassius Dio	is the only source for a portrayal of the course of the Battle of the Teutoburg Forest. He lived not only one – like Tacitus and Florus – but in fact two centuries after the fact, but probably had completely unfettered access to all official reports. Historians argue about whether this time depth obscured the picture for him or even partially illuminated it, since upholding the lies of war propaganda would no longer have been so important that much later. On this site, we have lent him great credence – as many others do; however, there is also an important tendency which questions his report, and this difference of viewpoints is the source of many Debates, which are addressed on this Site – but not here. As to the events in the war prior to the before the Battle of the Teutoburg Fores, Dio provides some important information; on the later course of the war, he is, however, extremely reticent, which is somewhat surprising, since it was this period, even more than the Battle of the Teutoburg Forest itself, which Tiberius seems to have tried to cover up. Why then doesn't Dio describe the truth 200 years later?
Tacitus	is the “Great Enlightener,” who wrote during the “golden age” of the second century, and lambasted the tyrannical emperors of the first century. Since, however, his account begins only with Augustus’ death (14 AD), its description of events in Germany covers only the last part of the war. For this period, however, he is the only detailed source; moreover his report on the visit to the site of the Battle of the Teutoburg Forest by the army of Germanicus in 15 AD contains such important information on that battle that this passage alone is enough to raise him into the ranks of the “Big Four.” Tacitus contrasts imperial tyranny with the ideal of freedom of the Roman Republic. He has a fine point of departure with the contrast of Tiberius and Germanicus, his designated successor: Germanicus is the brave hero in the ancient classical sense, Tiberius is a sovereign engaged in increasingly arbitrary misrule, who envies his nephew his success. Moreover, Arminius and his Germans, too, get a favorable description, as worthy and brave opponents fighting for their freedom. Ultimately, Tacitus also makes clear, Arminius was “beyond a doubt Germany’s liberator.” ‘This statement must be seen in the light of the fact that Rome had white-washed the defeat in Germany, granting Germanicus a triumph and trumpeting the recovery of the lost legionary eagles. In a society where foreign geography was simply unknown, the average Roman could easily have been told that Germany was actually defeated, but that the Rhine, and not the Elbe had been chosen as the boundary – for who had any idea where those rivers flowed? Tacitus emphasizes the successes of Germanicus– or invents victories for him – in order to substantiate his thesis that Germanicus could have won the war, had Tiberius not recalled him. Nonetheless, it is possible to read between the lines and to discover that the campaigns of 15 and 16 AD were an unmitigated catastrophe. Tacitus hardly reports a battle in which the Romans are not described routinely as massacring the Germans “into the night” (or some such) – and then retreating, giving up their goals, or withdrawing to the Rhine much earlier than the seasons would have mandated. And yet: Without Tacitus’ report, we would have virtually no knowledge of this important part of the war, which – even more than the Battle of the Teutoburg Forest itself – was decisive, in that it truly determined what the outcome would be.
Additional Authors:
Strabon, the Greek geographer, reports – like Suetonius, but more briefly – on the whole course of the war, but also in a very “Rome-centered” manner, i.e., no description of the fighting, bur a detailed portrayal of Germanicus “triumph” in 17 AD. Titus Livius in a rare preserved passage on this topic, reports on the beginning of the war, up to the death of Drusus in 9 BC, probably at Hedemünden, Lower Saxony. Similar reports are available from the little-known author Valerius Maximus Better-known authors with only brief surviving passages include, in addition to Pliny the Elder (see above), Eutropius and Lucius Annaeus Seneca, who provide useful facts, but primarily on the early period of the Roman conquest; and also Paulus Orosius a late-Roman Christian, whose brief reports are likely copied from earlier authors whose work is described here. Another little-known author named Julius Obsequens has left us some very short descriptions. Other interesting writings include those of Publius Ovidius Naso, who, around the time of the Battle of the Teutoburg Forest, was exiled to the west coast of the Black Sea, and tried with some fairly obsequious patriotic verse on the German War to earn a reprieve for himself – unsuccessfully; as it turned out; while he provides no very useful information, his is the oldest mention of the Battle of the Teutoburg Forest that we have; and Sextus Julius Frontinius, Who, in his Stratagems, provides some details to the Battle of the Teutoburg Forest and the time directly after it. Of much less interest are the references by the mostly little known writers Flaccus, Propertius, Krinagoras, Manilius, Pomponius Mela, Hieronymus, Flavius Vegetius, and Aurelius Victor; the latter additionally represented by an abbreviated work accredited to a “pseudo,” in which the descriptions of Suetonius are repeated. Inscriptions Inscriptions: Krüger berichtet von nur 3 Inschriften, wovon eine lediglich den „Bezwinger der Germanen“ Drusus erwähnt. Die anderen beiden sind the famous Res Gestae inscription in Ankara in which Augustus describes his life's work, with his famous claim “germaniam pacavi” – “I pacified Germany” – obviously not a true fact, but still a good indication of his intentions. and the well-known “gravestone” of M. Caelius in the Rheinisches Landesmuseum in Bonn, Germany, created as a memorial to a centurion who fell in the Battle of the Teutoburg Forest, and whose bones were presumably never be interred under it. The former monument provides us with little more than a glimpse of Augustus’ feelings – i.e., that he probably had not come to terms with the loss of Germany; the latter inscription is our only solid evidence supporting the accepted theory that the XVIIIth Legion was among the units destroyed in the Battle of the Teutoburg Forest. The Titulus Tiburtinus of Tivoli, which describes the career of some Roman official whose identity is hotly disputed, but who may have been Varus, is not mentioned by Krüger. Nor does he describe any Coins, which also provide scraps of written information. Coins copper as coins with Varus’ counter-mark, found at Kalkriese Hill, or a coin from his time as Praetor in Africa,that shows his face. There is also a memorial coin from the first decade BC showing a child being given to Augustus by a German chieftain as a hostage. If the theory is true that Arminius was sent in childhood as a hostage to the Romans, this image might be the only evidence of that fact – if it does indeed depict him, which is an extremely speculative hypothesis. Germanic sources “Germanic sources” are of course generally considered to be non-existent; nonetheless, two are on occasion cited: The Gnitterheide a landscape near Bad Salzuflen, Westphalia, was, according to the travelogue of a 12th century Icelandic monk named Nikulas – a man who could have been familiar with Germanic tradition – the “place where Siegfried attacked the dragon.” That constitutes a connection, at least as far as the believers in the “Arminius-was-Siegfried” theory are concerned; more on that under Debates. If that’s true, of course, the entire Edda, the Scandinavian saga which is the major source for the Nibelung legend, in which Siegfried appears, is a quarry for bits and pieces of speculation about the Roman-German War.