For individual files use Media Library; for a complete library, use a hosting backup/file-access method or an appropriate export/backup workflow.
Step by Step
- For one file, open Media Library and the attachment details.
- Use the file URL or available download option to retrieve it.
- For the full library, identify the site's wp-content/uploads directory through hosting/file access or a backup.
- Preserve year/month folders if the site uses them.
- Keep a database/site backup if you may need to restore attachment relationships.
If That Doesn't Work
- WordPress's standard content export does not necessarily package every media binary into one downloadable archive.
- Do not delete the server copy until you have verified the backup.