Goodreads often has many translations listed under ”Editions”, though of course there’s no guarantee that it’s exhaustive.
The entry for this book includes Polish and Lithuanian editions as well as Russian and Vietnamese (but not Slovak): https://www.goodreads.com/book/show/7329537
If I am looking at the same place, those seem like translations of other books by the same author.
(Specifically, "Zerko żeglarz" is Sailor Zero, Нулик-мореход; and "Varastatud marki otsimas" seems maaaaaybe like Table of Lost-and-Found Numbers, Стол находок утерянных чисел.)
But generally, yes, translations of books by the same author is a relatively short list that can be examined step by step.
To my knowledge, there is currently no method that will generate a reasonably exhaustive list of all the languages a given book has been translated into. I use a combination of Worldcat, Wikipedia, Amazon and Google.
I noticed that Wikipedia has some links to bibliographical and other catalogues at the bottom of the author's page. After exploring them...
Discogs is a database of audio recordings, so if someone is also interested in audiobooks, they could find them here. (And, hypothetically, there could be a translation in both paper and audio version, so finding the audiobook here could point towards a paper book.) Levshin actually has some audio here, but not that one book.
Лаборатория Фантастики is probably trying to be the thing that I imagined, for science fiction and fantasy, but the data is very incomplete. It lists various editions of the book I am looking for (that is also interesting for me), but none of the translations.
Katalog der Deutschen Nationalbibliothek only contains German translations, but it found one!
Virtual International Authority File seems like it aggregates information from various national libraries, so it found the Russian and German versions of the book.
WorldCat only found the Russian book.
...well, I found one more translation, that's a success! But it's disappointing that the sources that know about the Vietnamese translation don't know about the German one, and vice versa, and no one outside Slovakia knows about the Slovak one. Basically, out of 3 translations (that I am aware of) any web source knows at most 1.
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I thought that I had a clever idea, and I put the names of both the German and Vietnamese translations in Google. Any page that contains them both is very likely the one I am looking for... oops, zero results found.
Probably-obvious question: you mention finding one of them in a library, but have you tried asking the librarians there for help? They might have more relevant expertise than the readership of Less Wrong...
That is a very good question actually, and no I haven't tried, so I will do that.
(I see "library" as a place to take books from for my kids, and I admit I forgot that there are actual humans working there who may know something about books...)
What is the best way to find whether a book was translated to other languages (and how are the translations called)?
I assumed that there would be some global database for that; it feels like something that obviously should exist -- if you already assign ISBNs to books, the logical next step is to make a database that contains them, plus some metadata, including "this is a translation of this" -- but unless I am missing something obvious, there is no such service.
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Here is a specific book I was recently looking for, but the question is general:
Author: Владимир Артурович Лёвшин (Vladimir Arturovich Levshin or Lyovshin)
Book title: Три дня в Карликании
So far I only know about translations to Vietnamese and Slovak; the former I found on Wikipedia (the author only has a Wikipedia page in Russian and Vietnamese), the later because I happened to find that one in a library -- I couldn't find out about it otherwise.
(It is a book about math, for small kids. A very good one, if my memories are reliable.)