Once you have translated the files using editor, you can download them from Translated Languages section.
If you have multiple master files, translated files are organized in folders. You can navigate them by just clicking the language name. To get back root folder, just click the .. link. If you have just single master file, you can download the files directly.
Download selected languagesas as a ZIP file let's you download all the files in one ZIP. Just tap the languages you wish to download and click it.
You can also use the integration tools you can find from your project settings, for example Get Localization Command-Line Interface.