Last year Ukrainian support was added for Shadow of Chernobyl, Call of Pripyat, and Clear Sky. When you go to change the language in GOG Galaxy, it isn't an option (either in "Configure" or by launching "Additional executables -> Settings"). I see that when you go to Extras, you can download "Ukrainian localization", but this still doesn't add options to Configure or Settings.

Downloading "Ukrainian localization" gets you a zip file in the !Downloads folder of the game. When you unzip it, you get different things based on the game, but usually some game files and a ReadMe.txt in Russian. I have tried placing the game files where I think they should go, but they cause the game to crash and get corrupted.

Does anyone have a guide on how to get the Ukrainian localization working? Thanks

Some mistake by GOG it seems. Original and still available instructions on Ukrainian are available on GSC website along with original UA pack archive.
Should be no issue extracting files to the game. Except the first game. UA require RU version, and not compatible with original MULTI us/eu release. And first game here on GOG still use this separately alteration: MULTI version and RU. You need RU installer. Or russian language pack installed first (there was such ones too).

Two other games are MULTI+RU and UA can be installed easily on any.