My understanding is that Tacitus's Annals is extant in a single manuscript from a copy made in a German monastery around 1000 CE. While historians disagree on the accuracy of the document in its details, it seems like there is a general consensus that the document is a mostly accurate copy of an authentic work from the period claimed.
Is my understanding accurate? If so, what is the basis for the assumption that the document's contents are an authentic Roman work from around 100 CE? How do we know it isn't an inventive literary work from 300 CE, or a derivative version of an authentic work so heavily edited and altered as to be unrecognizable from the original?
While I ask about the Annals specifically, my question really goes for any text that is not known from an edition produced close to its purported composition.
First you may be interested in my answer in the FAQ "Textual Criticism, or How We Know What That Old Book Really Said". Over the last 400 years we have refined a process called "textual criticism" that lets us reconstruct texts with a high degree of confidence; sometimes we get lucky and we can check our reconstructions against new papyri finds, and overwhelmingly our reconstructions are correct. It's not a perfect method, but you'll get the whole story in that answer.
About the Annales, I'm not sure who told you there was only one manuscript. It IS true that the first six books exist in only one 9th century manuscript, but books 9-16 survived in a separate 11th century manuscript, of which multiple 15th century copies were produced and survive.
Having so few manuscripts does make the job of the textual critic more difficult, but the method is reliable.
If you're wondering how we know it was Tacitus' writing at all, well, we know Plutarch for instance knew of books by Tacitus titled "Histories" and "Annals", and we know Tacitus' style from other works.
This isn't really different from any other ancient work. There are usually hundreds of years between the date of composition and the earliest extant manuscript. There are certainly no autographs outside things like papyri and the Vindolanda Tablets.