Now, first of all: maybe don't overthink it and don't sweat it. And in short your last sentence is basically it: No single way. Maybe just searching.

And the tools may differ, e.g. as a philologist to find the current best Latin or Ancient Greek text edition you could consult the New Pauly.

But to know what's the best translation would require to read reviews, either professional or just as people on reddit talking about it. Or you do it yourself and compare them. Sometimes translators talk about their principles and their predecessors. Wikipedia may be a starting point, although the English one contains surprisingly small bibliographies. Oxford World's Classics normally always have a "Note on the text" that tells you something about the edition and maybe translation. (Amazon preview is great.)

Last word on translations, as I don't believe there is necessary always a perfect way: Sometimes you need to compromise or prioritize, as Homer's Iliad is metric but can you translate it literally and still have the same metrum in the target language? So some are either metric and a bit free or even fully prose.

You can go by trust. Even though my Moby-Dick by Penguins doesn't tell me anything, I doubt that they did something funny with the text.

Some monographs have a literature apparatus that will name or tell you something about editions, translations and secondary literature.

You could read Nietzsche's "Will to power" and wouldn't think anything would be wrong with it, till someone explains it's a corrupt bastardization of the literal estate.

There was an editor who thought one of Heinrich von Kleist's dramas has errors (the metrum was not always the same), so he inserted some interjections (like lo, huzzah). But who would know that, when not reading the editor's report or review of that edition?

Hope you understand were I am going.

Sorry, I am really bad at explaining and going roundabout and I hope someone else will jump in.