There are a couple of answers to this question. The first is that we have a very small, but important list of texts that survive from antiquity, a few manuscripts (see the Vatican Virgil) and some papyrus documents, the largest cache of which were found in Oxyrhynchus, where the moisture content in the air for the last 2,000 years is so low that we have actual pieces of papyrus which ancient people wrote on We have, for example, a fair number of writing exercises where people copied Homer, so we know some texts this way.

For everything else, it’s a little more complicated. The primary method of handing down texts was in manuscript form. Medieval monasteries and to a lesser extent nobles interested in collecting libraries would have scribes physically copy ancient texts into new codices and transmit ancient texts thus way. Much more common than intentionally changing texts, scribal mistakes are rampant. Sometimes, the people copying the texts didn’t have a strong command of Latin or Greek. This led to copious amounts of misspellings, omissions of entire lines or sentences, the editing of texts to make them more grammatically correct, or other similar mistakes.

But to get more on track with your original question, there are a few techniques that modern scholars can use to figure out inaccuracies in texts. We often (but certainly not always) have multiple copies, so we can compare the various versions, which sometimes come from separate manuscript traditions (i.e. sometimes we have multiple copies of a manuscript from a single original copy that survived from antiquity long enough to be copied, and other times we have copies made from multiple originals surviving from antiquity long enough to be copied). Comparing the two, we can make educated guesses based on what is original and what is added.

If we have several writings by an author, it’s pretty easy for linguists to spot a fake. Often, lesser known authors would claim that the works they wrote were by famous people so they would enjoy wider circulation. For example, if you were a 4th c. B.C. philosopher, you might claim the work you wrote was by Plato or Aristotle so more people would read your work. Both of those authors had a very distinctive style, so even if you tried to imitate it, there’d still be enough of a difference for modern linguists to at least have a suspicion of inauthenticity.

But for everything else, we don’t know for sure. It seems likely, however, that most of what we have isn’t fabricated, just because what we have mostly follows Classical patterns of writhing that are hard to imitate by later writers, even if they were steeped in Medieval Latin or Greek.

Perhaps the largest “pollution” in our sources is that the vast majority of classical writings do not survive. Whether consciously determined to not have enough value to be copied (which was an incredibly expensive and time consuming activity) or simply forgotten about, we are missing at least 90% (some scholars argue we have lost more than 99%) of the written sources from antiquity.