I get into the question of faked sources here a bit, which is to say that outright fakes are less of an issue than you might think in a lot of historical research, with the caveat that I'm thinking mainly here of textual analysis and not spotting, say, whether a sword in a museum is what it claims to be, which is well outside my area of direct knowledge.

In a practical sense of undertaking your own historical research, I'd argue that spotting fakes is a less important skill than reflecting on the context of how you're finding the source in the first place. If you're just googling '15th century water polo' or whatever, it's worth being more skeptical of what you find on random websites compared to what you might find instead through the Oxford Handbook of Early Modern Aquatic Recreation, or through the website of a reputable institution such as a university, library or archive. If the information is being hosted by someone else, you need to consider a) whether they have been completely rigorous in sourcing their information, and may have committed serious errors or b) have outright malicious purposes in presenting disinformation.

As well as the host of the information, think about what information are they providing you. In particular, are they giving you the tools you'd need to find the original source yourself if you wanted to - not just basic information like the author and title, but where the original is held and the archival reference needed to locate it. Equally, how selective are they being in how they present and quote the material? One thing I remember from my Masters degree is looking at Holocaust denial websites, which reproduced text from real documents, but only ever specific, decontextualised passages, whereas the same documents were available in full (usually in a photographic form, which is much harder to alter and cut apart to create misleading impressions) from more reputable websites. In such instances, partial reproduction of sources is aimed at distorting your understanding of what the source means. More generally, if a source seems to be challenging well-established narratives, it's a sign to be extra cautious about what the source is or appears to show - if something flatly contradicts what we know from other sources, that's a sign that we need to take careful stock of the relative merits of the various sources, see how far their contrasting portrayals can be explained or reconciled, and ultimately consider whether this new source is credible or not. There is no shortcut to this process beyond building up the contextual and specialist knowledge required to make these kinds of interpretative judgements.